No Access

Foundational issues in $f (T)$ gravity theory

Alexey Golovnev

https://orcid.org/0000-0002-7821-1516

Centre for Theoretical Physics, British University in Egypt, 11837 El Sherouk, Cairo, Egypt

E-mail Address: agolovnev@yandex.ru

Corresponding author.

Search for more papers by this author

and

María-José Guzmán

Departamento de Física y Astronomía, Facultad de Ciencias, Universidad de La Serena, Av. Juan Cisternas 1200, 1720236 La Serena, Chile

Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia

E-mail Address: maria.j.guzman.m@gmail.com

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S0219887821400077Cited by:47 (Source: Crossref)

This article is part of the issue:

Special Issue on TeleGrav2020
Guest Editors: Christian Pfeifer, Martin Krššák, Tomi Koivisto, Sebastian Bahamonde, Manuel Hohmann, Laur Järv and Margus Saal

Abstract

We give a short review on the status of research on the theoretical foundations of $f (𝕋)$ gravity theories. We discuss recent results on perturbative and non-perturbative approaches, causality and degrees of freedom, and discuss future directions to follow.

Keywords:

AMSC: 83D05

References

1. R. Aldrovandi and J. G. Pereira , Teleparallel gravity : An introduction, Fundam. Theor. Phys. 173 (2013). Google Scholar
2. A. Golovnev, Introduction to teleparallel gravities, Institute of Physics, Belgrade, 18–23 September 2017, Belgrade, Serbia, pp. 219–236. Google Scholar
3. R. Ferraro and F. Fiorini , Modified teleparallel gravity: Inflation without inflaton, Phys. Rev. D 75 (2007) 084031. Crossref, Web of Science, Google Scholar
4. G. R. Bengochea and R. Ferraro , Dark torsion as the cosmic speed-up, Phys. Rev. D 79 (2009) 124019. Crossref, Web of Science, Google Scholar
5. M. Krššák and E. N. Saridakis , The covariant formulation of f(T) gravity, Class. Quantum Grav. 33(11) (2016) 115009. Crossref, Web of Science, Google Scholar
6. A. Golovnev, T. Koivisto and M. Sandstad , On the covariance of teleparallel gravity theories, Class. Quantum Grav. 34(14) (2017) 145013. Crossref, Web of Science, Google Scholar
7. M. Hohmann, L. Järv and U. Ualikhanova , Covariant formulation of scalar-torsion gravity, Phys. Rev. D 97(10) (2018) 104011. Crossref, Web of Science, Google Scholar
8. M. Krššák, R. J. van den Hoogen, J. G. Pereira, C. G. Boehmer and A. A. Coley , Teleparallel theories of gravity: Illuminating a fully invariant approach, Class. Quantum Grav. 36(18) (2019) 183001. Crossref, Web of Science, Google Scholar
9. A. Eichhorn, A. Platania and M. Schiffer , Lorentz invariance violations in the interplay of quantum gravity with matter, Phys. Rev. D 102 (2020) 026007. Crossref, Web of Science, Google Scholar
10. K. Bamba, S. Capozziello, M. De Laurentis, S. Nojiri and D. Sáez-Gómez , No further gravitational wave modes in $F (T)$ gravity, Phys. Lett. B 727 (2013) 194. Crossref, Web of Science, Google Scholar
11. Y. F. Cai, C. Li, E. N. Saridakis and L. Xue , $f (T)$ gravity after GW170817 and GRB170817A, Phys. Rev. D 97(10) (2018) 103513. Crossref, Web of Science, Google Scholar
12. B. Li, T. P. Sotiriou and J. D. Barrow , Large-scale structure in f(T) gravity, Phys. Rev. D 83 (2011) 104017. Crossref, Web of Science, Google Scholar
13. A. Golovnev and T. Koivisto , Cosmological perturbations in modified teleparallel gravity models, J. Cosmol. Astropart. Phys. 1811 (2018) 012. Crossref, Web of Science, Google Scholar
14. A. Golovnev , Perturbations in $f (T)$ cosmology and the spin connection, J. Cosmol. Astropart. Phys. 04 (2020) 014. Crossref, Web of Science, Google Scholar
15. S. Chen, J. B. Dent, S. Dutta and E. N. Saridakis , Cosmological perturbations in f(T) gravity, Phys. Rev. D 83 (2011) 023508. Crossref, Web of Science, Google Scholar
16. M. Hashim, W. El Hanafy, A. Golovnev and A. El-Zant, Toward a concordance teleparallel cosmology I: Background dynamics, preprint (2020), arXiv: 2010.14964. Google Scholar
17. J. Beltrán Jiménez, A. Golovnev, T. Koivisto and H. Veermäe, Minkowski space in $f (T)$ gravity, preprint (2020), arXiv: 2004.07536 [gr-qc]. Google Scholar
18. A. Golovnev and M. J. Guzmán, Non-trivial Minkowski backgrounds in f(T) gravity, preprint (2020), arXiv: 2012.00696 [gr-qc]. Google Scholar
19. A. Finch and J. L. Said , Galactic rotation dynamics in f(T) gravity, Eur. Phys. J. C 78(7) (2018) 560. Crossref, Web of Science, Google Scholar
20. S. Bahamonde, J. L. Said and M. Zubair , Solar system tests in modified teleparallel gravity, J. Cosmol. Astropart. Phys. 10 (2020) 024. Crossref, Web of Science, Google Scholar
21. M. L. Ruggiero and N. Radicella , Weak-field spherically symmetric solutiuons in f(T) gravity, Phys. Rev. D 91 (2015) 104014. Crossref, Web of Science, Google Scholar
22. M. Li, R. X. Miao and Y. G. Miao , Degrees of freedom of $f (T)$ gravity, J. High Energy Phys. 1107 (2011) 108. Crossref, Web of Science, Google Scholar
23. R. Ferraro and M. J. Guzmán , Hamiltonian formalism for f(T) gravity, Phys. Rev. D 97(10) (2018) 104028. Crossref, Web of Science, Google Scholar
24. R. Ferraro and M. J. Guzmán , Quest for the extra degree of freedom in $f (T)$ gravity, Phys. Rev. D 98(12) (2018) 124037. Crossref, Web of Science, Google Scholar
25. R. Ferraro and M. J. Guzmán , Pseudoinvariance and the extra degree of freedom in f(T) gravity, Phys. Rev. D 101(8) (2020) 084017. Crossref, Web of Science, Google Scholar
26. M. Blagojevic and J. M. Nester , Local symmetries and physical degrees of freedom in f(T) gravity: A Dirac Hamiltonian constraint analysis, Phys. Rev. D 102 (2020) 064025. Crossref, Web of Science, Google Scholar
27. D. Blixt, M. Hohmann and C. Pfeifer , On the gauge fixing in the Hamiltonian analysis of general teleparallel theories, Universe 5 (2019) 143. Crossref, Web of Science, Google Scholar
28. D. Blixt, M. J. Guzmán, M. Hohmann and C. Pfeifer, Review of the Hamiltonian analysis in teleparallel gravity, preprint (2020), arXiv: 2012.09180 [gr-qc]. Google Scholar
29. R. Ferraro and F. Fiorini , Remnant group of local Lorentz transformations in $f (T)$ theories, Phys. Rev. D 91(6) (2015) 064019. Crossref, Web of Science, Google Scholar
30. Y. C. Ong, K. Izumi, J. M. Nester and P. Chen , Problems with propagation and time evolution in f(T) gravity, Phys. Rev. D 88 (2013) 024019. Crossref, Web of Science, Google Scholar
31. W. Kopczyński , Problems with metric-teleparallel theories of gravitation, J. Phys. A: Math. Gen. 15 (1982) 493–506. Crossref, Google Scholar
32. J. M. Nester , Is there really a problem with the teleparallel theory?, Class. Quantum Grav. 5 (1988) 1003–1010. Crossref, Web of Science, Google Scholar
33. P. Chen, K. Izumi, J. M. Nester and Y. C. Ong , Remnant symmetry, propagation and evolution in $f$ (T) gravity, Phys. Rev. D 91(6) (2015) 064003. Crossref, Web of Science, Google Scholar
34. K. Izumi, J. A. Gu and Y. C. Ong , Acausality and nonunique evolution in generalized teleparallel gravity, Phys. Rev. D 89(8) (2014) 084025. Crossref, Web of Science, Google Scholar
35. R. J. Yang , Conformal transformation in $f (T)$ theories, Europhys. Lett. 93(6) (2011) 60001. Crossref, Google Scholar
36. M. Wright , Conformal transformations in modified teleparallel theories of gravity revisited, Phys. Rev. D 93(10) (2016) 103002. Crossref, Web of Science, Google Scholar
37. A. Golovnev and M. J. Guzmán , Disformal transformations in modified teleparallel gravity, Symmetry 12 (2020) 152. Crossref, Web of Science, Google Scholar
38. C. Bejarano, R. Ferraro and M. J. Guzmán , Kerr geometry in f(T) gravity, Eurphys. J. C 75 (2015) 77. Google Scholar
39. G. G. L. Nashed , Exact axially symmetric solution in f(T) gravity theory, Adv. High Energy Phys. 2014 (2014) 857936. Google Scholar
40. C. Bejarano, R. Ferraro and M. J. Guzmán , McVittie solution in f(T) gravity, Euro. Phys. J. C 77(12) (2017) 825. Crossref, Web of Science, Google Scholar