Research ArticleNo Access

An extended theory of gravity in a modified Riemann’s geometry

http://orcid.org/0000-0001-7652-1900

Department of Physics, University of Kara, Kara, 404, Togo

Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei 230026, P. R. China

E-mail Address: [email protected]

Search for more papers by this author

, and

Samuel Owusu

Department of Applied Physics, University for Development Studies, Navrongo Campus, Ghana

E-mail Address: [email protected]

Search for more papers by this author

https://doi.org/10.1142/S0219887819500671Cited by:4 (Source: Crossref)

Abstract

In this work, we study the evolution of an isotropic universe in an extended theory of gravity obtained geometrically by transforming the normal-gauge Lyra displacement vector field $ϕ^{μ}$ as a complex vectorial function depending on a dynamical scalar field $φ$ . By using the latest observational data, we observe that for $ω^{0} = - 0.98$ the universe starts accelerating at the critical scale factor $a_{ac} = 0.626$ which corresponds to a redshift of $z_{ac} \approx 0.6$ . We also find that the dark energy fluid considered in this model is a generalized fluid with equation of state $p = - ρ + F (ρ, a)$ .

Keywords:

PACS: 98.80.Jk, 98.80.−k, 95.36.

+

x, 04.50.Kd, 02.40.Ky

References

1. G. Lyra, Über eine modifikation der Riemannschen geometrie, Math. Z. 54 (1951) 52. Crossref, Google Scholar
2. H. Weyl, Gravitation und Elektrizität, Sitzber. Preuss. Akad. Wiss. (1918) 465–480. Google Scholar
3. D. K. Sen, A static cosmological model, Z. Phys. 149 (1957) 311. Crossref, Google Scholar
4. D. K. Sen, On geodesics of a modified Riemannian manifold, Can. Math. Bull. 3 (1960) 255. Crossref, Google Scholar
5. D. K. Sen and K. A. Dunn, A scalar-tensor theory of gravitation in a modified Riemann manifold, J. Math. Phys. 12 (1971) 578. Crossref, Web of Science, Google Scholar
6. D. K. Sen and J. R. Vanstone, On Weyl and Lyra manifolds, J. Math. Phys. 13 (1972) 990. Crossref, Web of Science, Google Scholar
7. E. Scheibe, Über einen verallgemeinerten affinen Zusammenhang, Math. Z. 57(1) (1952) 65–74. Crossref, Google Scholar
8. W. D. Halford, Cosmological theory based on Lyra’s geometry, Aust. J. Phys. 23 (1970) 863. Crossref, Web of Science, Google Scholar
9. W. D. Halford, Scalar-tensor theory of gravitation in Lyra manifold, J. Math. Phys. 13 (1972) 1699. Crossref, Web of Science, Google Scholar
10. J. Matyjasek, On Sen equations in arbitrary gauge, Astrophys. Space Sci. 207 (1993) 313. Crossref, Web of Science, Google Scholar
11. J. Matyjasek, Junction conditions and static fluid cylinders in Lyra’s geometry, Int. J. Theor. Phys. 33(4) (1994) 967–982. Crossref, Web of Science, Google Scholar
12. A. Beesham, FLRW cosmological models in Lyra’s manifold with time-dependent displacement field, Aust. J. Phys. 41 (1988) 833. Crossref, Web of Science, Google Scholar
13. A. Beesham, Vacuum Friedmann cosmology based on Lyra’s manifold, Astrophys. Space Sci. 127 (1986) 189. Crossref, Web of Science, Google Scholar
14. H. H. Soleng, Scalar-tensor theory of gravitation with spin–scalar–torsion coupling, Class. Quantum Grav. 5 (1988) 1489–1500. Crossref, Web of Science, Google Scholar
15. H. H. Soleng, Cosmologies based on Lyra’s geometry, Gen. Relativ. Gravit. 19(12) (1987) 1213. Crossref, Web of Science, Google Scholar
16. R. H. Hudgin, Generalizing Riemannian geometry, J. Math. Phys. 14(12) (1973) 1794–1799. Crossref, Web of Science, Google Scholar
17. E. B. Manoukian, Gravity and scaling, Phys. Rev. D 5 (1972) 2915–2922. Crossref, Web of Science, Google Scholar
18. A. Pradhan and A. K. Vishwakarma, A new class of LRS Bianchi type-I cosmological models in Lyra geometry, J. Geom. Phys. 49 (2004) 332–342; G. Mohanty, K. L. Mahanta and R. R. Sahoo, Non-existence of five dimensional perfect fluid cosmological model in Lyra manifold, Astrophys. Space Sci. 306 (2006) 269–272; G. Mohanty, K. L. Mahanta and B. K. Bishi, Five-dimensional cosmological models in Lyra geometry with time dependent displacement field, Astrophys. Space Sci. 310 (2007) 273–276; G. Mohanty, G. C. Samanta and K. L. Mahanta, Kaluza–Klein FRW cosmological models in Lyra manifold, Theoret. Appl. Mech. 36(2) (2009) 157–166; F. Rahaman, Higher-dimensional global monopole in Lyra’s geometry, Fizika B 11(4) (2002) 223–229; F. Rahaman, S. Chakraborty, S. Das, N. Begum, M. Hossain and J. Bera, Higher-dimensional string theory in Lyra geometry, Pramana-J. Phys. 60(3) (2003) 453; F. Rahaman, S. Das, N. Begum and M. Hossain, Higher dimensional homogeneous cosmology in Lyra geometry, Pramana-J Phys. 61(1) (2003) 153–159; R. M. Gad, Axially symmetric cosmological mesonic stiff fluid models in Lyra’s geometry, Can. J. Phys. 89 (2011) 773–778; T. Singh, Cosmic no-hair conjecture in Lyra’s manifold, Grav. Cosmol. 3(2,10) (1997) 130–132; R. M. Wald, Asymptotic behavior of homogeneous cosmological models in the presence of a positive cosmological constant, Phys. Rev. D 28 (1983) 2118–2120. Google Scholar
19. H. Hova, A dark energy model in Lyra manifold, J. Geom. Phys. 64 (2013) 146–154. Crossref, Web of Science, Google Scholar
20. V. K. Shchigolev and E. A. Semenova, Scalar field cosmology in Lyra’s geometry, Int. J. Adv. Astron. 3(2) (2015) 117–122, arXiv: 1203.0917. Crossref, Google Scholar
21. A. G. Riess et al., Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116 (1998) 1009, arXiv: 9805201v1. Crossref, Web of Science, Google Scholar
22. S. Perlmutter et al., Measurements of omega and lambda from 42 high-redshift supernovae, Astrophys. J. 517 (1999) 565–586, arXiv: 9812133v1. Crossref, Web of Science, Google Scholar
23. E. J. Copeland, M. Sami and S. Tsujikawa, Dynamics of dark energy, Int. J. Modern Phys. D 15 (2006) 1753–1936, arXiv: hep-th/0603057v3. Link, Web of Science, Google Scholar
24. O. Luongo and M. Muccino, Speeding up the universe using dust with pressure, Phys. Rev. D 98 (2018) 103520, arXiv: 1807.00180. Crossref, Web of Science, Google Scholar
25. S. Nojiri and S. D. Odintsov, Unified cosmic history in modified gravity: From $f (R)$ theory to Lorentz non-invariant models, Phys. Rep. 505 (2011) 59–144, arXiv: 1011.0544v4. Crossref, Web of Science, Google Scholar
26. S. Nojiri, S. D. Odintsov and V. K. Oikonomou, Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution, Phys. Rep. 692 (2017) 1–104, arXiv: 1705.11098v2. Crossref, Web of Science, Google Scholar
27. S. Nojiri and S. D. Odintsov, Modified gravity with negative and positive powers of the curvature: Unification of the inflation and of the cosmic acceleration, Phys. Rev. D 68 (2003) 123512, arXiv: 0307288v4. Crossref, Web of Science, Google Scholar
28. A. De Felice and S. Tsujikawa, $f (R)$ theories, Living Rev. Rel. 13(3) (2010), arXiv: 1002.4928v2. Google Scholar
29. W. Hu and I. Sawicki, Models of $f (R)$ cosmic acceleration that evade solar system tests, Phys. Rev. D 76 (2007) 064004. Crossref, Web of Science, Google Scholar
30. V. Muller, H. J. Schmidt and A. A. Starobinsky, The stability of the De Sitter space-time in fourth order gravity, Phys. Lett. B 202 (1988) 198–200. Crossref, Web of Science, Google Scholar
31. L. Amendola et al., Conditions for the cosmological viability of $f (R)$ dark energy models, Phys. Rev. D 75 (2007) 083504. Crossref, Web of Science, Google Scholar
32. A. A. Starobinsky, Disappearing cosmological constant in $f (R)$ gravity, J. Exp. Theor. Phys. Lett. 86 (2007) 157–163. Crossref, Web of Science, Google Scholar
33. L. Amendola, D. Polarski and S. Tsujikawa, Are $f (R)$ dark energy models cosmologically viable? Phys. Rev. Lett. 98 (2007) 131302. Crossref, Web of Science, Google Scholar
34. L. Amendola, D. Polarski and S. Tsujikawa, Power-laws $f (R)$ theories are cosmologically unacceptable, Int. J. Modern Phys. D 16 (2007) 1555–1561. Link, Web of Science, Google Scholar
35. S. Nojiri and S. D. Odintsov, Modified $f (R)$ gravity consistent with realistic cosmology: From a matter dominated epoch to a dark energy universe, Phys. Rev. D 74 (2006) 086005. Crossref, Web of Science, Google Scholar
36. S. Nojiri and S. D. Odintsov, Unifying inflation with $Λ$ CDM epoch in modified $f (R)$ gravity consistent with solar system tests, Phys. Lett. B 657 (2007) 238–245. Crossref, Web of Science, Google Scholar
37. S. Nojiri and S. D. Odintsov, Modified $f (R)$ gravity unifying $R^{m}$ inflation with the $Λ$ CDM epoch, Phys. Rev. D 77 (2008) 026007. Crossref, Web of Science, Google Scholar
38. G. Cognola et al., Class of viable modified $f (R)$ gravities describing inflation and the onset of accelerated expansion, Phys. Rev. D 77 (2008) 046009. Crossref, Web of Science, Google Scholar
39. Y.-F. Cai et al., $f (T)$ teleparallel gravity and cosmology, Rep. Prog. Phys. 79(4) (2016) 106901, arXiv: 1511.07586v2. Crossref, Web of Science, Google Scholar
40. Y.-F. Cai et al., Matter bounce cosmology with the $f (T)$ gravity, Class. Quantum Grav. 28 (2011) 215011, arXiv: 1104.4349v2. Crossref, Web of Science, Google Scholar
41. R. Ferraro and F. Fiorini, Modified teleparallel gravity: Inflation without inflaton, Phys. Rev. D 75 (2007) 084031, arXiv: gr-qc/0610067. Crossref, Web of Science, Google Scholar
42. G. R. Bengochea and R. Ferraro, Dark torsion as the cosmic speed-up, Phys. Rev. D 79 (2009) 124019, arXiv: 0812.1205. Crossref, Web of Science, Google Scholar
43. E. V. Linder, Einstein’s other gravity and the acceleration of the universe, Phys. Rev. D 81 (2010) 127301, arXiv: 1005.3039. Crossref, Web of Science, Google Scholar
44. P. V. Tretyakov, Cosmology in modified $f (R, T)$ -gravity, Eur. Phys. J. C 78(11) (2018) 896, arXiv: 1810.11313. Crossref, Web of Science, Google Scholar
45. M. J. S. Houndjo et al., Higher-derivative $f (R, □ R, T)$ theories of gravity, Int. J. Modern Phys. D 26 (2017) 1750024, arXiv: 1601.00196. Link, Web of Science, Google Scholar
46. S. Capozziello, R. D’Agostino and O. Luongo, Rational approximations of $f (R)$ cosmography through Padé polynomials, J. Cosmol. Astropart. Phys. 1805(5) (2018) 008, arXiv: 1709.08407. Crossref, Web of Science, Google Scholar
47. H. Abedi, S. Capozziello, R. D’Agostino and O. Luongo, Effective gravitational coupling in modified teleparallel theories, Phys. Rev. D 97 (2018) 084008, arXiv: 1803.07171. Crossref, Web of Science, Google Scholar
48. R. D’Agostino and O. Luongo, Growth of matter perturbations in non-minimal teleparallel dark energy, Phys. Rev. D 98 (2018) 124013, arXiv: 1807.10167. Crossref, Web of Science, Google Scholar
49. S. Nojiri and S. D. Odintsov, Inhomogeneous equation of state of the universe: Phantom era, future singularity and crossing the phantom barrier, Phys. Rev. D 72 (2005) 023003, arXiv: 0505215v4. Crossref, Web of Science, Google Scholar
50. I. Brevik and Ø. Grøn, Relativistic viscous universe models, arXiv:1409.8561v1. Google Scholar
51. K. Bamba, S. Capozziello, S. Nojiri and S. D. Odintsov, Dark energy cosmology: The equivalent description via different theoretical models and cosmography tests, Astrophys. Space Sci. 342 (2012) 155, arXiv: 1205.3421. Crossref, Web of Science, Google Scholar
52. S. D. Odintsov, V. K. Oikonomou and P. V. Tretyakov, Phase space analysis of the accelerating multi-fluid universe, Phys. Rev. D 96 (2017) 044022, arXiv: 1707.08661v1. Crossref, Web of Science, Google Scholar
53. V. K. Oikonomou, Inflation and bounce from classical and loop quantum cosmology imperfect fluids, Int. J. Modern Phys. D 26(10) (2017) 1750110, arXiv: 1703.09009v1. Link, Web of Science, Google Scholar
54. I. Brevik and A. V. Timoshkin, Dissipative universe-inflation with soft singularity, Int. J. Geom. Methods Mod. Phys. 14 (2017) 1750061, arXiv: 1612.06689v1. Link, Web of Science, Google Scholar
55. H. Hova and H. Yang, A dark energy model alternative to generalized Chaplygin gas, Int. J. Modern Phys. D 27(1) (2018) 1750178. Link, Web of Science, Google Scholar
56. H. Hova, Vacuum expansion in arbitrary-gauge Lyra geometry, Can. J. Phys. 92 (2014) 311–315. Crossref, Web of Science, Google Scholar
57. J. W. Moffat, Generalized Riemann spaces, Math. Proc. Cambridge Phil. Soc. 52 (1956) 623–625. Crossref, Google Scholar
58. (Planck Collab.) N. Aghanim et al., Planck 2018 results. VI, Cosmological parameters, arXiv:1807.06209. Google Scholar

Remember to check out the Most Cited Articles!
Check out new Mathematical Physics books in our Mathematics 2021 catalogue Featuring authors Bang-Yen Chen, John Baez, Matilde Marcolli and more!

Vol. 16, No. 05

Metrics

History

Received 18 October 2018

Accepted 26 February 2019

Published: 21 March 2019

Keywords

PDF download

Adblock Plus Instructions

Adblock Instructions

uBlock Origin Instructions

uBlock Instructions

Adguard Instructions

Brave Instructions

Adremover Instructions

Adblock Genesis Instructions

Super Adblocker Instructions

Ultrablock Instructions

Ad Aware Instructions

Ghostery Instructions

Firefox Tracking Protection Instructions

Duck Duck Go Instructions

Privacy Badger Instructions

Disconnect Instructions

Opera Instructions

System Upgrade on Tue, Oct 25th, 2022 at 2am (EDT)

An extended theory of gravity in a modified Riemann’s geometry

Abstract

References

Select your blocker:

Adblock Plus Instructions

Adblock Instructions

uBlock Origin Instructions

uBlock Instructions

Adguard Instructions

Brave Instructions

Adremover Instructions

Adblock Genesis Instructions

Super Adblocker Instructions

Ultrablock Instructions

Ad Aware Instructions

Ghostery Instructions

Firefox Tracking Protection Instructions

Duck Duck Go Instructions

Privacy Badger Instructions

Disconnect Instructions

Opera Instructions

System Upgrade on Tue, Oct 25th, 2022 at 2am (EDT)

An extended theory of gravity in a modified Riemann’s geometry

Abstract

References

Recommended