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Localization of matters coupled nonminimally to gravity on scalar thick branes (2307.12614v4)

Published 24 Jul 2023 in hep-th

Abstract: We are investigating the localization of matter that interacts nonminimally with gravity within thick braneworld models generated by a scalar bulk. Our review focuses on two models of scalar thick branes. The natural mechanism is used to analyze the localization of the fields. Without losing the point of field localization, we examine matter field localizations by considering the asymptotic behavior of the warp function on z towards infinity. Both massless and massive modes of the nonminimally coupled scalar field are localized on the brane in both models. When the coupling is minimal, the scalar field is localized for the massless mode. A nonminimally coupled vector field behaves similarly to the nonminimally coupled scalar field, the massless and massive modes in both models are localized. For a nonminimally coupled spinor field, in model 1, we observe localization of the spinor for massive mode, while in model 2, only the massless spinor field is localized.

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References (35)
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[2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. 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[2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bajc, B., Gabadadze, G.: Localization of matter and cosmological constant on a brane in anti de sitter space. Physics Letters B 474, 282–291 (2000) https://doi.org/10.1016/S0370-2693(00)00055-1 Jones et al. [2013] Jones, P., Muñoz, G., Singleton, D., Triyanta: Field localization and the nambu–jona-lasinio mass generation mechanism in an alternative five-dimensional brane model. Physical Review D 88, 025048 (2013) https://doi.org/10.1103/PhysRevD.88.025048 Wulandari et al. [2017] Wulandari, D., Triyanta, Kosasih, J.S., Singleton, D., Jones, P.: Localization of interacting fields in five-dimensional braneworld models. International Journal of Modern Physics A 32 (2017) https://doi.org/10.1142/S0217751X17501913 Wulandari et al. [2019] Wulandari, D., Triyanta, Kosasih, J.S., Singleton, D.: The field localization of yukawa interaction in a modified randall-sundrum model. Journal of Physics: Conference Series 1204, 012044 (2019) https://doi.org/10.1088/1742-6596/1204/1/012044 Liu [2018] Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Jones, P., Muñoz, G., Singleton, D., Triyanta: Field localization and the nambu–jona-lasinio mass generation mechanism in an alternative five-dimensional brane model. Physical Review D 88, 025048 (2013) https://doi.org/10.1103/PhysRevD.88.025048 Wulandari et al. [2017] Wulandari, D., Triyanta, Kosasih, J.S., Singleton, D., Jones, P.: Localization of interacting fields in five-dimensional braneworld models. International Journal of Modern Physics A 32 (2017) https://doi.org/10.1142/S0217751X17501913 Wulandari et al. [2019] Wulandari, D., Triyanta, Kosasih, J.S., Singleton, D.: The field localization of yukawa interaction in a modified randall-sundrum model. Journal of Physics: Conference Series 1204, 012044 (2019) https://doi.org/10.1088/1742-6596/1204/1/012044 Liu [2018] Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Wulandari, D., Triyanta, Kosasih, J.S., Singleton, D., Jones, P.: Localization of interacting fields in five-dimensional braneworld models. International Journal of Modern Physics A 32 (2017) https://doi.org/10.1142/S0217751X17501913 Wulandari et al. [2019] Wulandari, D., Triyanta, Kosasih, J.S., Singleton, D.: The field localization of yukawa interaction in a modified randall-sundrum model. Journal of Physics: Conference Series 1204, 012044 (2019) https://doi.org/10.1088/1742-6596/1204/1/012044 Liu [2018] Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Wulandari, D., Triyanta, Kosasih, J.S., Singleton, D.: The field localization of yukawa interaction in a modified randall-sundrum model. Journal of Physics: Conference Series 1204, 012044 (2019) https://doi.org/10.1088/1742-6596/1204/1/012044 Liu [2018] Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. 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Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. 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Journal of Physics: Conference Series 1204, 012044 (2019) https://doi.org/10.1088/1742-6596/1204/1/012044 Liu [2018] Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Wulandari, D., Triyanta, Kosasih, J.S., Singleton, D., Jones, P.: Localization of interacting fields in five-dimensional braneworld models. International Journal of Modern Physics A 32 (2017) https://doi.org/10.1142/S0217751X17501913 Wulandari et al. [2019] Wulandari, D., Triyanta, Kosasih, J.S., Singleton, D.: The field localization of yukawa interaction in a modified randall-sundrum model. Journal of Physics: Conference Series 1204, 012044 (2019) https://doi.org/10.1088/1742-6596/1204/1/012044 Liu [2018] Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Wulandari, D., Triyanta, Kosasih, J.S., Singleton, D.: The field localization of yukawa interaction in a modified randall-sundrum model. Journal of Physics: Conference Series 1204, 012044 (2019) https://doi.org/10.1088/1742-6596/1204/1/012044 Liu [2018] Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. 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[2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Wulandari, D., Triyanta, Kosasih, J.S., Singleton, D., Jones, P.: Localization of interacting fields in five-dimensional braneworld models. International Journal of Modern Physics A 32 (2017) https://doi.org/10.1142/S0217751X17501913 Wulandari et al. [2019] Wulandari, D., Triyanta, Kosasih, J.S., Singleton, D.: The field localization of yukawa interaction in a modified randall-sundrum model. Journal of Physics: Conference Series 1204, 012044 (2019) https://doi.org/10.1088/1742-6596/1204/1/012044 Liu [2018] Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Wulandari, D., Triyanta, Kosasih, J.S., Singleton, D.: The field localization of yukawa interaction in a modified randall-sundrum model. Journal of Physics: Conference Series 1204, 012044 (2019) https://doi.org/10.1088/1742-6596/1204/1/012044 Liu [2018] Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. 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Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. 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Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. 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[2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. 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  5. Wulandari, D., Triyanta, Kosasih, J.S., Singleton, D.: The field localization of yukawa interaction in a modified randall-sundrum model. Journal of Physics: Conference Series 1204, 012044 (2019) https://doi.org/10.1088/1742-6596/1204/1/012044 Liu [2018] Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. 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  6. Liu, Y.X.: Introduction to extra dimensions and thick braneworlds. Memorial Volume for Yi-shi Duan, 211–275 (2018) https://doi.org/10.1142/9789813237278_0008 Liu et al. [2008] Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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  7. Liu, Y.-X., Zhang, X.-H., Zhang, L.-D., Duan, Y.-S.: Localization of matters on pure geometrical thick branes. Journal of High Energy Physics 2008, 067–067 (2008) https://doi.org/10.1088/1126-6708/2008/02/067 Guo et al. [2013] Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. 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Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. 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  8. Guo, H., Herrera-Aguilar, A., Liu, Y.X., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of bulk matter fields, the hierarchy problem and corrections to coulomb’s law on a pure de sitter thick braneworld. Physical Review D 87, 1–21 (2013) https://doi.org/10.1103/PhysRevD.87.095011 Herrera-Aguilar et al. [2010] Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Herrera-Aguilar, A., Malagón-Morejón, D., Mora-Luna, R.R.: Localization of gravity on a de sitter thick braneworld without scalar fields. Journal of High Energy Physics 2010 (2010) https://doi.org/10.1007/JHEP11(2010)015 Liang and Duan [2009] Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. 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Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Liang, J., Duan, Y.-S.: Localization of matters on thick branes. Physics Letters B 678, 491–496 (2009) https://doi.org/10.1016/j.physletb.2009.06.067 Bazeia et al. [2009] Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. 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Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. 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Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. 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Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. 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Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. 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[2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. 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Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. 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Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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  11. Bazeia, D., Gomes, A.R., Losano, L.: Gravity localization on thick branes: A numerical approach. International Journal of Modern Physics A 24, 1135–1160 (2009) https://doi.org/10.1142/S0217751X09043067 Gremm [2000] Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. 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Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. 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[2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gremm, M.: Four-dimensional gravity on a thick domain wall. Physics Letters B 478, 434–438 (2000) https://doi.org/10.1016/S0370-2693(00)00303-8 Geng and Lü [2016] Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. 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Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. 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[2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Geng, W.-J., Lü, H.: Einstein-vector gravity, emerging gauge symmetry, and de sitter bounce. Physical Review D 93 (2016) https://doi.org/10.1103/PhysRevD.93.044035 Dzhunushaliev and Folomeev [2011] Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Dzhunushaliev, V., Folomeev, V.: Spinor brane. General Relativity and Gravitation 43, 1253–1261 (2011) https://doi.org/10.1007/s10714-010-1105-2 Cui and Liu [2023] Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. 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[2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. 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Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. 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Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. 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Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. 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Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. 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[2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. 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  15. Cui, Z.-Q., Liu, Y.-X.: Spinor walls in five-dimensional warped spacetime. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11422-0 Bazeia et al. [2014] Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. 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Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. 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  16. Bazeia, D., Lobão, A.S., Menezes, R., Petrov, A., Silva, A.J.: Braneworld solutions for f(r) models with non-constant curvature. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 729, 127–135 (2014) https://doi.org/10.1016/j.physletb.2014.01.011 Bazeia et al. [2015] Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. 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European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bazeia, D., Lobão, A.S., Menezes, R.: Thick brane models in generalized theories of gravity. Physics Letters B 743, 98–103 (2015) https://doi.org/10.1016/j.physletb.2015.02.037 Gu et al. [2017] Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. 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Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Gu, B.M., Zhang, Y.P., Yu, H., Liu, Y.X.: Full linear perturbations and localization of gravity on f(r, t) brane. European Physical Journal C 77 (2017) https://doi.org/10.1140/epjc/s10052-017-4666-3 Rohman and Triyanta [2021] Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. 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Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. 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Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. 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Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. 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Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. 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Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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  19. Rohman, M.T., Triyanta: Localization of scalar field on f(r, t) thick robertson-walker brane. Journal of Physics: Conference Series 1816, 012058 (2021) https://doi.org/10.1088/1742-6596/1816/1/012058 Bezrukov and Shaposhnikov [2008] Bezrukov, F., Shaposhnikov, M.: The standard model higgs boson as the inflaton. Physics Letters B 659, 703–706 (2008) https://doi.org/10.1016/j.physletb.2007.11.072 Harko and Lobo [2014] Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. 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Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. 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Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Harko, T., Lobo, F.S.N.: Generalized curvature-matter couplings in modified gravity. Galaxies 2, 410–465 (2014) https://doi.org/10.3390/galaxies2030410 Farakos and Pasipoularides [2005] Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 621, 224–232 (2005) https://doi.org/10.1016/j.physletb.2005.06.058 Farakos and Pasipoularides [2006] Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. 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[2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. 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[2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. 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Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. 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Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. 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Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. 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Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. 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Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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[2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Gravity-induced instability and gauge field localization. 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Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Farakos, K., Pasipoularides, P.: Second randall-sundrum brane world scenario with a nonminimally coupled bulk scalar field. Physical Review D - Particles, Fields, Gravitation and Cosmology 73 (2006) https://doi.org/10.1103/PhysRevD.73.084012 Guo et al. [2012] Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. 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Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. 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Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. 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[2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. 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[2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. 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[2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. 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Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. 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  24. Guo, H., Liu, Y.X., Zhao, Z.H., Chen, F.W.: Thick branes with a nonminimally coupled bulk-scalar field. Physical Review D 85 (2012) https://doi.org/10.1103/PhysRevD.85.124033 Moazzen and Ghalenovi [2017] Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3
  25. Moazzen, M., Ghalenovi, Z.: Non-minimally coupled bulk scalar fields in sine–gordon braneworld models. Annals of Physics 385, 70–85 (2017) https://doi.org/10.1016/j.aop.2017.08.006 Zhao et al. [2023] Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. 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Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. 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Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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  26. Zhao, Z.-H., Xie, Q.-Y., Fu, C.-E., Zhou, X.-N.: Localization of u(1) gauge field by non-minimal coupling with gravity in braneworlds. Journal of Cosmology and Astroparticle Physics 2023 (2023) https://doi.org/10.1088/1475-7516/2023/07/010 Moreira et al. [2023] Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. 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Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. 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Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3
  27. Moreira, A.R.P., Belchior, F.M., Maluf, R.V., Almeida, C.A.S.: Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario. European Physical Journal C 83 (2023) https://doi.org/10.1140/epjc/s10052-023-11213-7 Zhong and Sui [2024] Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3
  28. Zhong, Y., Sui, T.-T.: Localization of q-form fields on a de sitter brane in chameleon gravity. Frontiers of Physics 19 (2024) https://doi.org/10.1007/s11467-023-1361-8 Zhou and Guo [2023] Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3
  29. Zhou, X.-N., Guo, W.-Q.: Localization of gravitino field with non-minimal coupling on a thick brane. Physica Scripta 98 (2023) https://doi.org/10.1088/1402-4896/ad0527 DeWolfe et al. [2000] DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 DeWolfe, O., Freedman, D.Z., Gubser, S.S., Karch, A.: Modeling the fifth dimension with scalars and gravity. Physical Review D - Particles, Fields, Gravitation and Cosmology (2000) https://doi.org/10.1103/PhysRevD.62.046008 Nambu and Jona-Lasinio [1961] Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3
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  31. Nambu, Y., Jona-Lasinio, G.: Dynamical model of elementary particles based on an analogy with superconductivity. i. Physical Review 122, 345–358 (1961) https://doi.org/10.1103/PhysRev.122.345 Cruz et al. [2016] Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3
  32. Cruz, W.T., Maluf, R.V., Sousa, L.J.S., Almeida, C.A.S.: Gravity localization in sine-gordon braneworlds. Annals of Physics 364, 25–34 (2016) https://doi.org/10.1016/j.aop.2015.10.016 Davoudiasl et al. [2000] Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3
  33. Davoudiasl, H., Hewett, J.L., Rizzo, T.G.: Bulk gauge fields in the randall-sundrum model. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 473, 43–49 (2000) https://doi.org/10.1016/S0370-2693(99)01430-6 Guerrero and Rodriguez [2019] Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3
  34. Guerrero, R., Rodriguez, R.O.: Fermions localization on de sitter branes. Physical Review D 100, 104038 (2019) https://doi.org/10.1103/PhysRevD.100.104038 Oda [2000] Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3 Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3
  35. Oda, I.: Localization of matters on a string-like defect. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 496, 113–121 (2000) https://doi.org/10.1016/S0370-2693(00)01284-3

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