Papers
Topics
Authors
Recent
Search
2000 character limit reached

Dynamical System Analysis for Scalar Field Potential in Teleparallel Gravity

Published 16 May 2024 in gr-qc and hep-th | (2405.10354v1)

Abstract: In this paper, we have presented a power law cosmological model and its dynamical system analysis in $f(T,\phi)$ gravity, where $T$ is the torsion scalar and $\phi$ is the canonical scalar field. The two well-motivated forms of the non-minimal coupling function $F(\phi)$, the exponential form and the power law form, with exponential potential function, are investigated. The dynamical system analysis is performed by establishing the dimensionless dynamical variables, and the critical points were obtained. The evolution of standard density parameters is analysed for each case. The behaviour of the equation of state (EoS) and deceleration parameter show agreement with the result of cosmological observations. The model parameters are constrained using the existence and the stability conditions of the critical points describing different epochs of the evolution of the Universe.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (46)
  1. E. Di Valentino, A. Melchiorri, and J. Silk, “Reconciling Planck with the local value of H0subscript𝐻0H_{0}italic_H start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT in extended parameter space,” Phys. Lett. B 761 (2016) 242–246, arXiv:1606.00634 [astro-ph].
  2. E. J. Copeland, M. Sami, and S. Tsujikawa, “Dynamics of dark energy,” Int. J. Mod. Phys. D 15 (2006) 1753–1936, arXiv:hep-th/0603057 [hep-th].
  3. J. Martin, “Everything you always wanted to know about the cosmological constant problem (but were afraid to ask),” Compt. Rend. Phys. 13 (2012) no. 6–7, , arXiv:1205.3365 [astro-ph].
  4. S. Tsujikawa, “Quintessence: A Review,” Class. Quant. Grav. 30 (2013) 214003, arXiv:1304.1961 [gr-qc].
  5. T. Chiba, T. Okabe, and M. Yamaguchi, “Kinetically driven quintessence,” Phys. Rev. D 62 (2000) 023511, arXiv:astro-ph/9912463 [astro-ph].
  6. C. Armendariz-Picon, V. F. Mukhanov, and P. J. Steinhardt, “Essentials of k essence,” Phys. Rev. D 63 (2001) 103510, arXiv:astro-ph/0006373 [astro-ph].
  7. N. Roy and N. Bhadra, “Dynamical systems analysis of phantom dark energy models,” JCAP 2018 (2018) 002, arXiv:1710.05968 [gr-qc].
  8. G. Otalora, “Cosmological dynamics of tachyonic teleparallel dark energy,” Phys. Rev. D 88 (2013) 063505, arXiv:1305.5896 [gr-qc].
  9. A. Sen, “Rolling tachyon,” JHEP 2002 (2002) no. 04, , arXiv:0203211 [hep-th].
  10. Y.-F. Cai, E. N. Saridakis, M. R. Setare, and J.-Q. Xia, “Quintom Cosmology: Theoretical implications and observations,” Phys. Rept. 493 (2010) 1–60, arXiv:0909.2776 [hep-th].
  11. No. pt. 3 in Gravitation. W. H. Freeman, 1973. https://books.google.com.mt/books?id=w4Gigq3tY1kC.
  12. R. Weitzenböock, ‘Invariantentheorie’. Noordhoff, Gronningen, 1923.
  13. K. Hayashi and T. Shirafuji, “New General Relativity,” Phys. Rev. D 19 (1979) 3524–3553. [Addendum: Phys.Rev.D 24, 3312–3314 (1982)].
  14. E. V. Linder, “Einstein’s Other Gravity and the Acceleration of the Universe,” Phys. Rev. D 81 (2010) 127301, arXiv:1005.3039 [astro-ph.CO]. [Erratum: Phys.Rev.D 82, 109902 (2010)].
  15. R. Ferraro and F. Fiorini, “Modified teleparallel gravity: Inflation without inflaton,” Phys. Rev. D 75 (2007) 084031, arXiv:gr-qc/0610067 [gr-qc].
  16. Y.-F. Cai, S. Capozziello, M. De Laurentis, and E. N. Saridakis, “f⁢(T)𝑓𝑇f(T)italic_f ( italic_T ) teleparallel gravity and cosmology,” Rept. Prog. Phys. 79 (2016) no. 10, 106901, arXiv:1511.07586 [gr-qc].
  17. G. R. Bengochea and R. Ferraro, “Dark torsion as the cosmic speed-up,” Phys. Rev. D 79 (2009) 124019, arXiv:0812.1205 [astro-ph].
  18. L. K. Duchaniya, S. V. Lohakare, B. Mishra, and S. K. Tripathy, “Dynamical stability analysis of accelerating f⁢(T)𝑓𝑇f(T)italic_f ( italic_T ) gravity models,” Eur. Phys. J. C 82 (2022) no. 5, 448, arXiv:2202.08150 [gr-qc].
  19. S. Basilakos, S. Nesseris, F. K. Anagnostopoulos, and E. N. Saridakis, “Updated constraints on f⁢(T)𝑓𝑇f(T)italic_f ( italic_T ) models using direct and indirect measurements of the Hubble parameter,” JCAP 08 (2018) 008, arXiv:1803.09278 [astro-ph.CO].
  20. L. K. Duchaniya and Kanika Gandhi and B. Mishra, “Attractor behavior of f⁢(T)𝑓𝑇f(T)italic_f ( italic_T ) modified gravity and the cosmic acceleration,” Phys. Dark Univ. 44 (2024) 101461, arXiv:2303.09076 [gr-qc].
  21. S. Capozziello and M. De Laurentis, “Extended Theories of Gravity,” Phys. Rept. 509 (2011) 167–321, arXiv:1108.6266 [gr-qc].
  22. S. Bahamonde, C. G. Böhmer, S. Carloni, E. J. Copeland, W. Fang, and N. Tamanini, “Dynamical systems applied to cosmology: dark energy and modified gravity,” Phys. Rept. 775-777 (2018) 1–122, arXiv:1712.03107 [gr-qc].
  23. C.-Q. Geng, C.-C. Lee, E. N. Saridakis, and Y.-P. Wu, “Teleparallel dark energy,” Phys. Lett. B 704 (2011) 384–387, arXiv:1109.1092 [hep-th].
  24. C.-Q. Geng, C.-C. Lee, and E. N. Saridakis, “Observational constraints on teleparallel dark energy,” JCAP 2012 (2012) , arXiv:1110.0913v2 [astro-ph].
  25. R. Ferraro and F. Fiorini, “On Born-Infeld Gravity in Weitzenbock spacetime,” Phys. Rev. D 78 (2008) 124019, arXiv:0812.1981 [gr-qc].
  26. J.-P. Uzan, “Cosmological scaling solutions of nonminimally coupled scalar fields,” Phys. Rev. D 59 (1999) no. 12, , arXiv:9903004 [gr-qc].
  27. L. Amendola, “Scaling solutions in general nonminimal coupling theories,” Phys. Rev. D 60 no. 4, , arXiv:9904120 [astro-ph].
  28. M. Gonzalez-Espinoza, G. Otalora, and J. Saavedra, “Stability of scalar perturbations in scalar-torsion f⁢(T,ϕ)𝑓𝑇italic-ϕf(T,\phi)italic_f ( italic_T , italic_ϕ ) gravity theories in the presence of a matter fluid,” JCAP 10 (2021) 007, arXiv:2101.09123 [gr-qc].
  29. M. Gonzalez-Espinoza, R. Herrera, G. Otalora, and J. Saavedra, “Reconstructing inflation in scalar-torsion f⁢(T,ϕ)𝑓𝑇italic-ϕf(T,\phi)italic_f ( italic_T , italic_ϕ ) gravity,” EPJC 81 (2021) no. 8, , arXiv:2106.06145 [gr-qc].
  30. M. Gonzalez-Espinoza and G. Otalora, “Cosmological dynamics of dark energy in scalar-torsion f⁢(T,ϕ)𝑓𝑇italic-ϕf(T,\phi)italic_f ( italic_T , italic_ϕ ) gravity,” Eur. Phys. J. C 81 (2021) no. 5, 480, arXiv:2011.08377 [gr-qc].
  31. M. Hohmann, L. Järv, and U. Ualikhanova, “Covariant formulation of scalar-torsion gravity,” Phys. Rev. D 97 (2018) no. 10, 104011, arXiv:1801.05786 [gr-qc].
  32. O. Trivedi, M. Khlopov, J. L. Said, and R. C. Nunes, “Cosmological singularities in f⁢(T,ϕ)𝑓𝑇italic-ϕf(T,\phi)italic_f ( italic_T , italic_ϕ ) gravity,” EPJC 83 (2023) 1017, arXiv:2310.20222 [gr-qc].
  33. S. A. Kadam, B. Mishra, and J. Said Levi, “Teleparallel scalar-tensor gravity through cosmological dynamical systems,” Eur. Phys. J. C 82 (2022) no. 8, 680, arXiv:2205.04231 [gr-qc].
  34. S. A. Kadam, N. P. Thakkar, and B. Mishra, “Dynamical system analysis in teleparallel gravity with boundary term,” Eur. Phys. J. C 83 (2023) no. 9, , arXiv:2306.06677 [gr-qc].
  35. L. K. Duchaniya, S. A. Kadam, J. L. Said, and B. Mishra, “Dynamical systems analysis in f⁢(T,ϕ)𝑓𝑇italic-ϕf(T,\phi)italic_f ( italic_T , italic_ϕ ) gravity,” Eur. Phys. J. C 83 (2023) no. 1, 27, arXiv:2209.03414 [gr-qc].
  36. L. K. Duchaniya, S. V. Lohakare, and B. Mishra, “Cosmological models in f⁢(T,𝒯)𝑓𝑇𝒯f(T,\mathcal{T})italic_f ( italic_T , caligraphic_T ) gravity and the dynamical system analysis,” Phys. Dark Univ. 43 (2024) 101402, arXiv:2302.07132 [gr-qc].
  37. S. A. Kadam, S. V. Lohakare, and B. Mishra, “Dynamical complexity in teleparallel gauss–bonnet gravity,” Annals of Physics 460 (2024) 169563, arXiv:2303.16911 [gr-qc].
  38. A. Paliathanasis, “de Sitter and Scaling solutions in a higher-order modified teleparallel theory,” JCAP 08 (2017) 027, arXiv:1706.02662 [gr-qc].
  39. S. S. da Costa, F. V. Roig, J. S. Alcaniz, S. Capozziello, M. D. Laurentis, and M. Benetti, “Dynamical analysis on f⁢(R,G)𝑓𝑅𝐺f(R,G)italic_f ( italic_R , italic_G ) cosmology,” Class. Quan. Grav. 35 (2018) no. 7, 075013, arXiv:1802.02572 [gr-qc].
  40. A. Samaddar and S. S. Singh, “Qualitative stability analysis of cosmological models in f⁢(T,ϕ)𝑓𝑇italic-ϕf(T,\phi)italic_f ( italic_T , italic_ϕ ) gravity,” Gen. Relat. Grav. 55 (2023) no. 10, 111.
  41. P. Wu and H. W. Yu, “The dynamical behavior of f⁢(T)𝑓𝑇f(T)italic_f ( italic_T ) theory,” Phys. Lett. B 692 (2010) 176–179, arXiv:1007.2348 [astro-ph.CO].
  42. B. Mirza and F. Oboudiat, “Constraining f⁢(T)𝑓𝑇f(T)italic_f ( italic_T ) gravity by dynamical system analysis,” JCAP 2017 (2017) no. 11, 011–011, arXiv::1704.02593 [gr-qc].
  43. R. Briffa, C. Escamilla-Rivera, J. L. Said, and J. Mifsud, “Constraints on f⁢(T)𝑓𝑇f(T)italic_f ( italic_T ) cosmology with Pantheon+,” MNRAS 522 (2023) 6024–6034, arXiv:2303.13840v1 [gr-qc].
  44. Springer Science & Business Media, 2003.
  45. G. Otalora, “Scaling attractors in interacting teleparallel dark energy,” JCAP 07 (2013) 044, arXiv:1305.0474 [gr-qc].
  46. S. Capozziello, R. D’Agostino, and O. Luongo, “High-redshift cosmography: auxiliary variables versus Padé polynomials,” MNRAS 494 (2020) 2576–2590, arXiv:2003.09341 [astro-ph].
Citations (1)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 1 tweet with 0 likes about this paper.

Sign Up for Free