Abstract
In this paper, we investigate the effects of torsion and shears within the framework of the gravitational field with torsion in early and late cosmology. General relativity and torsion field equations are constructed using absolute parallel geometry. The Big Rip model of the Universe has been presented using a special class of Riemann–Cartan geometry and the law of variation of Hubble’s parameter. The model does not depend on the curvature constant. The positive condition of the energy density of the matter is satisfied in this model. This cosmological model shows that the torsion and shear effect is strong at the beginning of the Big Bang and at the end of the universe. Through the examination of precise cases of the parameters and initial conditions, we can show that for suitable ranges of the parameters, the dynamic torsion scalar model can exhibit features similar to those of the currently observed accelerating universe. The relationship between the torsion and shear scalars is investigated, and their impact on the accelerating universe is addressed apart from the idea of dark energy.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Change history
07 April 2023
The original version of this article has been revised: a typo in authors’ affiliations 2 and 4 has been corrected.
06 April 2023
A Correction to this paper has been published: https://doi.org/10.1007/s10509-023-04188-0
References
Akarsu, Ö., Tekin, D.: Int. Theor. Phys. 51(2), 612 (2012)
Aldrovandi, R., Pereira, J.G.: Teleparallel Gravity: An Introduction. Springer, Dordrecht (2012)
Astier, P., et al.: Astron. Astrophys. 447(1), 31 (2006)
Bakry, M.A., et al.: Indian J. Phys. (2021). https://doi.org/10.1007/s12648-020-01980-4
Bakry, M.A., Shafeek, A.A.: Astrophys. Space Sci. 364, 135 (2019)
Bakry, M.A., Shafeek, A.T.: Grav. Cosm. J. 27, 89–104 (2021). https://doi.org/10.1134/S0202289321010047
Bento, M.C., Bertolami, O., Sen, A.A.: Phys. Rev. D 66(4), 043507 (2002)
Berman, M.S.: Il Nuovo Cimento B (1971–1996) 74(2), 182 (1983)
Berman, M.S., de Mello Gomide, F.: Gen. Relativ. Gravit. 20(2), 191 (1988)
Brans, C., Robert, H.D.: Phys. Rev. 124(3), 925 (1961)
Cahill, K.: Phys. Rev. D 102(6), 065011 (2020)
Caldwell, R.R., Kamionkowski, M., Weinberg, N.N.: Phys. Rev. Lett.91, 071301 (2003)
Capozziello, S., et al.: Quantum Gravity 24(24), 6417 (2007)
Capozziello, S., De Falco, V., Pincak, R.: Int. J. Geom. Methods Mod. Phys. 14(12), 1750186 (2017)
Cartan, E.: Ann. Sci. Éc. Norm. Supér. 40, 325 (1923)
Chui, T.C.P., Ni, W.T.: Phys. Rev. Lett. 71(20), 3247 (1993)
Cruz, M., Izaurieta, F., Lepe, S.: Eur. Phys. J. C 80(6), 1 (2020)
Cunha, J.V.: Phys. Rev. D 79, 047301 (2009)
Cunha, J.V., Lima, J.A.S.: Mon. Not. R. Astron. Soc. 390, 210 (2008)
Dagwal, V.J., Pawar, D.D.: Mod. Phys. Lett. A 33(36), 1850213 (2018). 2018
David, R., et al.: Mon. Not. R. Astron. Soc. 375(4), 1510 (2007)
de Bernardis, P., et al.: Nature 404(6781), 955 (2000)
Dimitrios, K., et al.: Eur. Phys. J. C 79(4), 1 (2019)
Einstein, A.: Math. Ann. 102, 685 (1930)
Frieman, J., Turner, M., Huterer, D.: Annu. Rev. Astron. Astrophys. 46, 385 (2008)
Geroch, R.P.: J. Math. Phys. 8(4), 782 (1967)
Geroch, R.P.: Ann. Phys. 48(3), 526 (1968a)
Geroch, R.P.: J. Math. Phys. 9(3), 450 (1968b)
Hammond, T.R.: Rep. Prog. Phys. 5, 599 (2002)
Heavens, A.F., Kitching, T.D., Taylorn, A.N.: Mon. Not. R. Astron. Soc. 373(1), 105 (2006)
Hehl, F.W., Obukhov, Y.N.: ArXiv preprint (2007). 0711.1535
Hehl, F.W., et al.: Rev. Mod. Phys. 48(3), 393 (1976)
Hehl, W.F., Obukhov, Y.N., Puetzfeld, D.: Phys. Lett. A 377(31–33), 1775 (2013)
Ishida, E.E.O., Reis, R.R.R., Toribio, A.V., Waga, I.: Astropart. Phys. 28, 547 (2008)
Kibble, T.W.: J. Math. Phys. 2(2), 212 (1961)
Knop, R.A., et al.: Astrophys. J. 598(1), 102 (2003)
Kostelecký, V.A., Alan Russell, N., Tasson, J.D.: Phys. Rev. Lett. 100(11), 111102 (2008)
Kranas, D., Tsagas, C.G., Barrow, J.D., Iosifidis, D.: Eur. Phys. J. C 79(4), 1 (2019)
Li, Z., Wu, P., Yu, H.: Phys. Lett. B 695, 1–4 (2011)
Lima, J.A.S., Holanda, R.F.L., Cunha, J.V.: AIP Conf. Proc. 1241, 224 (2010)
Lin, R.-H., Zhai, X.-H., Li, X.-Z.: Eur. Phys. J. C 77(8), 504 (2017)
Lu, J., Chee, G.L., J. High Energy Phys. 2016(5), 1 (2016)
Mao, Y., et al.: Phys. Rev. D 76(10), 104029 (2007)
March, R., Bellettini, G., Tauraso, S., et al.: Phys. Rev. D 83, 10104008 (2011)
Mikhail, F.I.: Ain Shams Sci. Bull. 6, 87–111 (1962)
Mikhail, F.I., Wanas, M.I.: Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 356(1687), 471 (1977)
Mishra, R.K., et al.: Eur. Phys. J. Plus 127, 137 (2012)
Mishra, R.K., et al.: Int. J. Theor. Phys. 52, 2546 (2013a)
Mishra, R.K., et al.: Rom. J. Phys. 58, 75 (2013b)
Mukhanov, A.C.V., Steinhardt, P.J.: Phys. Rev. D 63(10), 103510 (2001)
Narlikar, J.V.: Lectures on General Relativity and Cosmology. p. Itd.PP260. Macmillan, London (1979) Itd.PP260
Ni, W.T.: Class. Quantum Gravity 13(11), A135 (1996)
Nojiri, S., Sergei, D.O.: Phys. Lett. B 562(3–4), 147 (2003)
Pandolfi, S.: Nucl. Phys. B 194, 294 (2009)
Pawar, D.D., Solanke, Y.S.: Int. J. Theor. Phys. 53(9), 3052 (2014)
Pawar, D.D., Shahare, S.P., Dagwal, V.J.: New Astron. 87(9), 101599 (2021).
Pereira, S.H., Lima, R.D.C., Jesus, J.F., Holanda, R.F.L.: Eur. Phys. J. C 79(11), 1 (2019)
Perlmutter, S., Brian, P.S.: Measuring cosmology with supernovae. In: Supernova and Gamma-Ray Bursters, pp. 195–217. Springer, Berlin (2003)
Perlmutter, S., et al.: Astrophys. J. 517(2), 565 (1999)
Puetzfeld, D., Obukhov, Y.N.: Int. J. Mod. Phys. D 23(12), 1442004 (2014)
Rabin, B., Chakraborty, S., Mukherjee, P.: Phys. Rev. D 98(8), 083506 (2018)
Ratra, B., Philip, J.E.P.: Phys. Rev. D 37(12), 3406 (1988)
Riess, A.G., et al.: Astron. J. 116(3), 1009 (1998)
Riess, A.G., et al.: Astrophys. J. 607(2), 665 (2004)
Riess, A.G., et al.: Astrophys. J. 659, 98 (2007)
Robertson, H.P.: Ann. Math. 496, 33 (1932)
Sahoo, P.K., Sivakumar, M.: Astrophys. Space Sci. 357(1), 60 (2015)
Sahoo, P.K., Tripathy, S.K., Sahoo, P.: Mod. Phys. Lett. A 33(33), 1850193 (2018)
Sciama, D.W.: Festschrift for Leopold Infeld. Pergamon, New York (1962)
Siamak, A., Qorani, E., Khajenabi, F.: Europhys. Lett. 119(2), 29002 (2017)
Spergel, D.N., et al.: Astrophys. J. Suppl. Ser. 148(1), 175 (2003)
Spergel, D.N., et al.: Astrophys. J. Suppl. Ser. 170(2), 377 (2007)
Taylor, P.L., et al.: Phys. Rev. D 98(2), 023522 (2018)
Toporensky, A.V., Tretyakov, P.V.: Phys. Rev. D 102(4), 044049 (2020)
Trautman, A.: Math. Astron. Phys. 20(185), 503 (1972)
Vignolo, S., Fabbri, L.: Int. J. Geom. Methods Mod. Phys. 9(07), 1250054 (2012)
Visser, M.: Class. Quantum Gravity 21(11), 2603 (2004)
Wanas, M.I.: Symposium-International Astronomical Union, vol. 168. Cambridge University Press, Cambridge (1996)
Wanas, M.I.: Turk. J. Phys. 24(3), 473 (2000)
Wanas, M.I.: Int. J. Mod. Phys. A 22(31), 5709 (2007)
Wanas, M.I.: An alternative source for dark energy. In: The Eleventh Marcel Grossmann Meeting: On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (2008). (In 3 Volumes)
Wanas, M.I.: ArXiv preprint (2010). 1006.2154
Wanas, M.I., Bakry, M.A.: Int. J. Mod. Phys. A 24(27), 5025 (2009)
Wanas, M.I., Hassan, H.A.: Int. J. Theor. Phys. 53(11), 3901 (2014)
Wanas, M.I., Ammar, S.A., Refaey, S.A.: Can. J. Phys. 96(12), 1373 (2018a)
Wanas, M.I., Samah, A.A., Refaey, S.A.: Can. J. Phys. 96(12), 1373 (2018a)
Wanas, M.I., Kamal, M.M., Dabash, T.F.: Eur. Phys. J. Plus 133(1), 1 (2018b)
Wolfgang, H., Niemeyer, J.C.: Annu. Rev. Astron. Astrophys. 38(1), 191 (2000)
Xiao, K., Wang, S.Q.: Mod. Phys. Lett. A 35(35), 2050293 (2020)
Yo, H.J., Nester, J.M.: Int. J. Mod. Phys. D 8(04), 459 (1999). https://doi.org/10.1142/S021827189900033X
Acknowledgements
The authors extend their appreciation to the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University, KSA for funding this work through Research Group no. RG-21-09-42. Also, the authors would like to express their deep gratitude to Prof. M. I. Wanas and Prof. M. I. Kahil for their deep interest and valuable comments during extraction of this work.
Funding
This research was funded by Imam Mohammad Ibn Saud Islamic University, KSA, Research Group no. RG-21-09-42.
Author information
Authors and Affiliations
Contributions
Conceptualization: M. A. Bakry and A. Eid; investigation: M. A. Bakry, A. Eid, and M. M. Khader; methodology: M. A. Bakry and A. Eid; formal analysis: M. A. Bakry and A. Eid; writing: M. A. Bakry and A. Eid; validation: M. A. Bakry, A. Eid, and M. M. Khader. All authors have read and agreed to the published version of the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The original version of this article has been revised: a typo in authors’ affiliations 2 and 4 has been corrected.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Bakry, M.A., Eid, A. & Khader, M.M. Torsion and shear effect on a Big Rip model in a gravitational field. Astrophys Space Sci 366, 97 (2021). https://doi.org/10.1007/s10509-021-04002-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10509-021-04002-9