Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Field transformations and invariant quantities in scalar-teleparallel theories of gravity (2312.17609v2)

Published 29 Dec 2023 in gr-qc

Abstract: We study transformations of the dynamical fields - a metric, a flat affine connection and a scalar field - in scalar-teleparallel gravity theories. The theories we study belong either to the general teleparallel setting, where no further condition besides vanishing curvature is imposed on the affine connection, or the symmetric or metric teleparallel gravity, where one also imposes vanishing torsion or nonmetricity, respectively. For each of these three settings, we find a general class of scalar-teleparallel action functionals which retain their form under the aforementioned field transformations. This is achieved by generalizing the constraint of vanishing torsion or nonmetricity to non-vanishing, but algebraically constrained torsion or nonmetricity. We find a number of invariant quantities which characterize these theories independently of the choice of field variables, and relate these invariants to analogues of the conformal frames known from scalar-curvature gravity. Using these invariants, we are able to identify a number of physically relevant subclasses of scalar-teleparallel theories. We also generalize our results to multiple scalar fields, and speculate on further extended theories with non-vanishing, but algebraically constrained curvature.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (61)
  1. T. Baker, D. Psaltis, and C. Skordis, Linking Tests of Gravity On All Scales: from the Strong-Field Regime to Cosmology, Astrophys. J. 802, 63 (2015), arXiv:1412.3455 [astro-ph.CO] .
  2. N. Aghanim et al. (Planck), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO] .
  3. S. Nojiri and S. D. Odintsov, Introduction to modified gravity and gravitational alternative for dark energy, eConf C0602061, 06 (2006), arXiv:hep-th/0601213 .
  4. S. Nojiri and S. D. Odintsov, Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models, Phys. Rept. 505, 59 (2011), arXiv:1011.0544 [gr-qc] .
  5. V. Faraoni and S. Capozziello, Beyond Einstein Gravity: A Survey of Gravitational Theories for Cosmology and Astrophysics (Springer, Dordrecht, 2011).
  6. L. Heisenberg, A systematic approach to generalisations of General Relativity and their cosmological implications, Phys. Rept. 796, 1 (2019), arXiv:1807.01725 [gr-qc] .
  7. C. Pfeifer and C. Lämmerzahl, eds., Modified and Quantum Gravity: From Theory to Experimental Searches on All Scales (Springer, Cham, 2023).
  8. M. Hohmann, Teleparallel Gravity, Lect. Notes Phys. 1017, 145 (2023), arXiv:2207.06438 [gr-qc] .
  9. J. W. Maluf, The teleparallel equivalent of general relativity, Annalen Phys. 525, 339 (2013), arXiv:1303.3897 [gr-qc] .
  10. J. M. Nester and H.-J. Yo, Symmetric teleparallel general relativity, Chin. J. Phys. 37, 113 (1999), arXiv:gr-qc/9809049 .
  11. C. G. Boehmer and E. Jensko, Modified gravity: A unified approach, Phys. Rev. D 104, 024010 (2021), arXiv:2103.15906 [gr-qc] .
  12. S. Capozziello, V. De Falco, and C. Ferrara, Comparing equivalent gravities: common features and differences, Eur. Phys. J. C 82, 865 (2022), arXiv:2208.03011 [gr-qc] .
  13. L. Heisenberg, Review on f⁢(Q)𝑓𝑄f(Q)italic_f ( italic_Q ) Gravity,   (2023), arXiv:2309.15958 [gr-qc] .
  14. T. Damour and G. Esposito-Farese, Tensor multiscalar theories of gravitation, Class. Quant. Grav. 9, 2093 (1992).
  15. V. Faraoni, Cosmology in scalar tensor gravity, Vol. 139 (Springer, 2004).
  16. Y. Fujii and K. Maeda, The scalar-tensor theory of gravitation (Cambridge University Press, 2007).
  17. E. V. Linder, Einstein’s Other Gravity and the Acceleration of the Universe, Phys. Rev. D 81, 127301 (2010), [Erratum: Phys.Rev.D 82, 109902 (2010)], arXiv:1005.3039 [astro-ph.CO] .
  18. C.-Q. Geng, C.-C. Lee, E. N. Saridakis, and Y.-P. Wu, “Teleparallel” dark energy, Phys. Lett. B 704, 384 (2011), arXiv:1109.1092 [hep-th] .
  19. M. Hohmann, L. Järv, and U. Ualikhanova, Covariant formulation of scalar-torsion gravity, Phys. Rev. D 97, 104011 (2018), arXiv:1801.05786 [gr-qc] .
  20. M. Hohmann, Scalar-torsion theories of gravity I: general formalism and conformal transformations, Phys. Rev. D 98, 064002 (2018a), arXiv:1801.06528 [gr-qc] .
  21. M. Hohmann, Scalar-torsion theories of gravity III: analogue of scalar-tensor gravity and conformal invariants, Phys. Rev. D98, 064004 (2018b), arXiv:1801.06531 [gr-qc] .
  22. M. Rünkla and O. Vilson, Family of scalar-nonmetricity theories of gravity, Phys. Rev. D 98, 084034 (2018), arXiv:1805.12197 [gr-qc] .
  23. L. Heisenberg, M. Hohmann, and S. Kuhn, Homogeneous and isotropic cosmology in general teleparallel gravity, Eur. Phys. J. C 83, 315 (2023), arXiv:2212.14324 [gr-qc] .
  24. E. E. Flanagan, The Conformal frame freedom in theories of gravitation, Class. Quant. Grav. 21, 3817 (2004), arXiv:gr-qc/0403063 [gr-qc] .
  25. R. Catena, M. Pietroni, and L. Scarabello, Einstein and Jordan reconciled: a frame-invariant approach to scalar-tensor cosmology, Phys. Rev. D 76, 084039 (2007), arXiv:astro-ph/0604492 .
  26. V. Faraoni and S. Nadeau, The (pseudo)issue of the conformal frame revisited, Phys. Rev. D75, 023501 (2007), arXiv:gr-qc/0612075 [gr-qc] .
  27. N. Deruelle and M. Sasaki, Conformal equivalence in classical gravity: the example of ’Veiled’ General Relativity, Springer Proc. Phys. 137, 247 (2011), arXiv:1007.3563 [gr-qc] .
  28. T. Chiba and M. Yamaguchi, Conformal-Frame (In)dependence of Cosmological Observations in Scalar-Tensor Theory, JCAP 10, 040, arXiv:1308.1142 [gr-qc] .
  29. M. Postma and M. Volponi, Equivalence of the Einstein and Jordan frames, Phys. Rev. D 90, 103516 (2014), arXiv:1407.6874 [astro-ph.CO] .
  30. V. Faraoni, E. Gunzig, and P. Nardone, Conformal transformations in classical gravitational theories and in cosmology, Fund. Cosmic Phys. 20, 121 (1999), arXiv:gr-qc/9811047 [gr-qc] .
  31. S. Capozziello, P. Martin-Moruno, and C. Rubano, Physical non-equivalence of the Jordan and Einstein frames, Phys. Lett. B 689, 117 (2010), arXiv:1003.5394 [gr-qc] .
  32. F. Rondeau and B. Li, Equivalence of cosmological observables in conformally related scalar tensor theories, Phys. Rev. D 96, 124009 (2017), arXiv:1709.07087 [gr-qc] .
  33. C. Wetterich, Quantum scale symmetry,   (2019), arXiv:1901.04741 [hep-th] .
  34. J. Bamber, Fifth forces and frame invariance, Phys. Rev. D 107, 024013 (2023), arXiv:2210.06396 [gr-qc] .
  35. S. Chakraborty, A. Mazumdar, and R. Pradhan, Distinguishing Jordan and Einstein frames in gravity through entanglement,  (2023), arXiv:2310.06899 [gr-qc] .
  36. P. Kuusk, L. Jarv, and O. Vilson, Invariant quantities in the multiscalar-tensor theories of gravitation, Int. J. Mod. Phys. A31, 1641003 (2016a), arXiv:1509.02903 [gr-qc] .
  37. A. Karam, T. Pappas, and K. Tamvakis, Frame-dependence of higher-order inflationary observables in scalar-tensor theories, Phys. Rev. D96, 064036 (2017), arXiv:1707.00984 [gr-qc] .
  38. A. Golovnev and T. Koivisto, Cosmological perturbations in modified teleparallel gravity models, JCAP 11, 012, arXiv:1808.05565 [gr-qc] .
  39. A. Golovnev and M.-J. Guzmán, Foundational issues in f(T) gravity theory, Int. J. Geom. Meth. Mod. Phys. 18, 2140007 (2021), arXiv:2012.14408 [gr-qc] .
  40. M. Blagojević and J. M. Nester, Local symmetries and physical degrees of freedom in f⁢(T)𝑓𝑇f(T)italic_f ( italic_T ) gravity: a Dirac Hamiltonian constraint analysis, Phys. Rev. D 102, 064025 (2020), arXiv:2006.15303 [gr-qc] .
  41. M. J. Guzmán and R. Ferraro, Degrees of freedom and Hamiltonian formalism for f⁢(T)𝑓𝑇f(T)italic_f ( italic_T ) gravity, Int. J. Mod. Phys. A 35, 2040022 (2020), arXiv:1910.03100 [gr-qc] .
  42. J. Beltrán Jiménez and K. F. Dialektopoulos, Non-Linear Obstructions for Consistent New General Relativity, JCAP 01, 018, arXiv:1907.10038 [gr-qc] .
  43. A. Golovnev and M.-J. Guzman, Nontrivial Minkowski backgrounds in f⁢(T)𝑓𝑇f(T)italic_f ( italic_T ) gravity, Phys. Rev. D 103, 044009 (2021), arXiv:2012.00696 [gr-qc] .
  44. M. Li and H. Rao, Irregular universe in the Nieh-Yan modified teleparallel gravity, Phys. Lett. B 841, 137929 (2023), arXiv:2301.02847 [gr-qc] .
  45. D. Iosifidis and T. Koivisto, Scale transformations in metric-affine geometry, Universe 5, 82 (2019), arXiv:1810.12276 [gr-qc] .
  46. M. Hohmann and U. Ualikhanova, Post-Newtonian limit of generalized scalar-teleparallel theories of gravity,  (2023), arXiv:2312.13352 [gr-qc] .
  47. M. Hohmann, Variational Principles in Teleparallel Gravity Theories, Universe 7, 114 (2021), arXiv:2104.00536 [gr-qc] .
  48. E. D. Emtsova and M. Hohmann, Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories, Phys. Rev. D 101, 024017 (2020), arXiv:1909.09355 [gr-qc] .
  49. K. Flathmann and M. Hohmann, Post-Newtonian Limit of Generalized Scalar-Torsion Theories of Gravity, Phys. Rev. D 101, 024005 (2020), arXiv:1910.01023 [gr-qc] .
  50. K. Flathmann and M. Hohmann, Parametrized post-Newtonian limit of generalized scalar-nonmetricity theories of gravity, Phys. Rev. D 105, 044002 (2022), arXiv:2111.02806 [gr-qc] .
  51. M. Gell-Mann and M. Levy, The axial vector current in beta decay, Nuovo Cim. 16, 705 (1960).
  52. S. Bahamonde, K. F. Dialektopoulos, and J. Levi Said, Can Horndeski Theory be recast using Teleparallel Gravity?, Phys. Rev. D 100, 064018 (2019), arXiv:1904.10791 [gr-qc] .
  53. G. W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10, 363 (1974).
  54. T. Kobayashi, M. Yamaguchi, and J. Yokoyama, Generalized G-inflation: Inflation with the most general second-order field equations, Prog. Theor. Phys. 126, 511 (2011), arXiv:1105.5723 [hep-th] .
  55. T. Kobayashi, Horndeski theory and beyond: a review, Rept. Prog. Phys. 82, 086901 (2019), arXiv:1901.07183 [gr-qc] .
  56. J. D. Bekenstein, The Relation between physical and gravitational geometry, Phys. Rev. D 48, 3641 (1993), arXiv:gr-qc/9211017 .
  57. D. Bettoni and S. Liberati, Disformal invariance of second order scalar-tensor theories: Framing the Horndeski action, Phys. Rev. D 88, 084020 (2013), arXiv:1306.6724 [gr-qc] .
  58. J. M. Ezquiaga, J. García-Bellido, and M. Zumalacárregui, Field redefinitions in theories beyond Einstein gravity using the language of differential forms, Phys. Rev. D 95, 084039 (2017), arXiv:1701.05476 [hep-th] .
  59. M. Zumalacárregui and J. García-Bellido, Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian, Phys. Rev. D 89, 064046 (2014), arXiv:1308.4685 [gr-qc] .
  60. M. Hohmann, Disformal Transformations in Scalar-Torsion Gravity, Universe 5, 167 (2019), arXiv:1905.00451 [gr-qc] .
  61. A. Golovnev and M. J. Guzman, Disformal transformations in modified teleparallel gravity, Symmetry 12, 152 (2020), arXiv:1912.04604 [gr-qc] .

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now