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Torsion and shear effect on a Big Rip model in a gravitational field

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.

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References

  1. Akarsu, Ö., Tekin, D.: Int. Theor. Phys. 51(2), 612 (2012)

    Google Scholar 

  2. Aldrovandi, R., Pereira, J.G.: Teleparallel Gravity: An Introduction. Springer, Dordrecht (2012)

    MATH  Google Scholar 

  3. Astier, P., et al.: Astron. Astrophys. 447(1), 31 (2006)

    ADS  Google Scholar 

  4. Bakry, M.A., et al.: Indian J. Phys. (2021). https://doi.org/10.1007/s12648-020-01980-4

    Article  Google Scholar 

  5. Bakry, M.A., Shafeek, A.A.: Astrophys. Space Sci. 364, 135 (2019)

    ADS  Google Scholar 

  6. Bakry, M.A., Shafeek, A.T.: Grav. Cosm. J. 27, 89–104 (2021). https://doi.org/10.1134/S0202289321010047

    Article  ADS  Google Scholar 

  7. Bento, M.C., Bertolami, O., Sen, A.A.: Phys. Rev. D 66(4), 043507 (2002)

    ADS  Google Scholar 

  8. Berman, M.S.: Il Nuovo Cimento B (1971–1996) 74(2), 182 (1983)

    ADS  Google Scholar 

  9. Berman, M.S., de Mello Gomide, F.: Gen. Relativ. Gravit. 20(2), 191 (1988)

    ADS  Google Scholar 

  10. Brans, C., Robert, H.D.: Phys. Rev. 124(3), 925 (1961)

    MathSciNet  ADS  Google Scholar 

  11. Cahill, K.: Phys. Rev. D 102(6), 065011 (2020)

    MathSciNet  ADS  Google Scholar 

  12. Caldwell, R.R., Kamionkowski, M., Weinberg, N.N.: Phys. Rev. Lett.91, 071301 (2003)

    ADS  Google Scholar 

  13. Capozziello, S., et al.: Quantum Gravity 24(24), 6417 (2007)

    MathSciNet  Google Scholar 

  14. Capozziello, S., De Falco, V., Pincak, R.: Int. J. Geom. Methods Mod. Phys. 14(12), 1750186 (2017)

    MathSciNet  Google Scholar 

  15. Cartan, E.: Ann. Sci. Éc. Norm. Supér. 40, 325 (1923)

    Google Scholar 

  16. Chui, T.C.P., Ni, W.T.: Phys. Rev. Lett. 71(20), 3247 (1993)

    ADS  Google Scholar 

  17. Cruz, M., Izaurieta, F., Lepe, S.: Eur. Phys. J. C 80(6), 1 (2020)

    ADS  Google Scholar 

  18. Cunha, J.V.: Phys. Rev. D 79, 047301 (2009)

    ADS  Google Scholar 

  19. Cunha, J.V., Lima, J.A.S.: Mon. Not. R. Astron. Soc. 390, 210 (2008)

    ADS  Google Scholar 

  20. Dagwal, V.J., Pawar, D.D.: Mod. Phys. Lett. A 33(36), 1850213 (2018). 2018

    ADS  Google Scholar 

  21. David, R., et al.: Mon. Not. R. Astron. Soc. 375(4), 1510 (2007)

    ADS  Google Scholar 

  22. de Bernardis, P., et al.: Nature 404(6781), 955 (2000)

    ADS  Google Scholar 

  23. Dimitrios, K., et al.: Eur. Phys. J. C 79(4), 1 (2019)

    Google Scholar 

  24. Einstein, A.: Math. Ann. 102, 685 (1930)

    MathSciNet  Google Scholar 

  25. Frieman, J., Turner, M., Huterer, D.: Annu. Rev. Astron. Astrophys. 46, 385 (2008)

    ADS  Google Scholar 

  26. Geroch, R.P.: J. Math. Phys. 8(4), 782 (1967)

    MathSciNet  ADS  Google Scholar 

  27. Geroch, R.P.: Ann. Phys. 48(3), 526 (1968a)

    ADS  Google Scholar 

  28. Geroch, R.P.: J. Math. Phys. 9(3), 450 (1968b)

    MathSciNet  ADS  Google Scholar 

  29. Hammond, T.R.: Rep. Prog. Phys. 5, 599 (2002)

    ADS  Google Scholar 

  30. Heavens, A.F., Kitching, T.D., Taylorn, A.N.: Mon. Not. R. Astron. Soc. 373(1), 105 (2006)

    ADS  Google Scholar 

  31. Hehl, F.W., Obukhov, Y.N.: ArXiv preprint (2007). 0711.1535

  32. Hehl, F.W., et al.: Rev. Mod. Phys. 48(3), 393 (1976)

    ADS  Google Scholar 

  33. Hehl, W.F., Obukhov, Y.N., Puetzfeld, D.: Phys. Lett. A 377(31–33), 1775 (2013)

    MathSciNet  ADS  Google Scholar 

  34. Ishida, E.E.O., Reis, R.R.R., Toribio, A.V., Waga, I.: Astropart. Phys. 28, 547 (2008)

    ADS  Google Scholar 

  35. Kibble, T.W.: J. Math. Phys. 2(2), 212 (1961)

    ADS  Google Scholar 

  36. Knop, R.A., et al.: Astrophys. J. 598(1), 102 (2003)

    MathSciNet  ADS  Google Scholar 

  37. Kostelecký, V.A., Alan Russell, N., Tasson, J.D.: Phys. Rev. Lett. 100(11), 111102 (2008)

    ADS  Google Scholar 

  38. Kranas, D., Tsagas, C.G., Barrow, J.D., Iosifidis, D.: Eur. Phys. J. C 79(4), 1 (2019)

    Google Scholar 

  39. Li, Z., Wu, P., Yu, H.: Phys. Lett. B 695, 1–4 (2011)

    ADS  Google Scholar 

  40. Lima, J.A.S., Holanda, R.F.L., Cunha, J.V.: AIP Conf. Proc. 1241, 224 (2010)

    ADS  Google Scholar 

  41. Lin, R.-H., Zhai, X.-H., Li, X.-Z.: Eur. Phys. J. C 77(8), 504 (2017)

    ADS  Google Scholar 

  42. Lu, J., Chee, G.L., J. High Energy Phys. 2016(5), 1 (2016)

    Google Scholar 

  43. Mao, Y., et al.: Phys. Rev. D 76(10), 104029 (2007)

    ADS  Google Scholar 

  44. March, R., Bellettini, G., Tauraso, S., et al.: Phys. Rev. D 83, 10104008 (2011)

    Google Scholar 

  45. Mikhail, F.I.: Ain Shams Sci. Bull. 6, 87–111 (1962)

    Google Scholar 

  46. Mikhail, F.I., Wanas, M.I.: Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 356(1687), 471 (1977)

    ADS  Google Scholar 

  47. Mishra, R.K., et al.: Eur. Phys. J. Plus 127, 137 (2012)

    Google Scholar 

  48. Mishra, R.K., et al.: Int. J. Theor. Phys. 52, 2546 (2013a)

    Google Scholar 

  49. Mishra, R.K., et al.: Rom. J. Phys. 58, 75 (2013b)

    Google Scholar 

  50. Mukhanov, A.C.V., Steinhardt, P.J.: Phys. Rev. D 63(10), 103510 (2001)

    ADS  Google Scholar 

  51. Narlikar, J.V.: Lectures on General Relativity and Cosmology. p. Itd.PP260. Macmillan, London (1979) Itd.PP260

    Google Scholar 

  52. Ni, W.T.: Class. Quantum Gravity 13(11), A135 (1996)

    ADS  Google Scholar 

  53. Nojiri, S., Sergei, D.O.: Phys. Lett. B 562(3–4), 147 (2003)

    ADS  Google Scholar 

  54. Pandolfi, S.: Nucl. Phys. B 194, 294 (2009)

    Google Scholar 

  55. Pawar, D.D., Solanke, Y.S.: Int. J. Theor. Phys. 53(9), 3052 (2014)

    Google Scholar 

  56. Pawar, D.D., Shahare, S.P., Dagwal, V.J.: New Astron. 87(9), 101599 (2021).

    Google Scholar 

  57. Pereira, S.H., Lima, R.D.C., Jesus, J.F., Holanda, R.F.L.: Eur. Phys. J. C 79(11), 1 (2019)

    Google Scholar 

  58. Perlmutter, S., Brian, P.S.: Measuring cosmology with supernovae. In: Supernova and Gamma-Ray Bursters, pp. 195–217. Springer, Berlin (2003)

    Google Scholar 

  59. Perlmutter, S., et al.: Astrophys. J. 517(2), 565 (1999)

    ADS  Google Scholar 

  60. Puetzfeld, D., Obukhov, Y.N.: Int. J. Mod. Phys. D 23(12), 1442004 (2014)

    ADS  Google Scholar 

  61. Rabin, B., Chakraborty, S., Mukherjee, P.: Phys. Rev. D 98(8), 083506 (2018)

    MathSciNet  ADS  Google Scholar 

  62. Ratra, B., Philip, J.E.P.: Phys. Rev. D 37(12), 3406 (1988)

    ADS  Google Scholar 

  63. Riess, A.G., et al.: Astron. J. 116(3), 1009 (1998)

    ADS  Google Scholar 

  64. Riess, A.G., et al.: Astrophys. J. 607(2), 665 (2004)

    ADS  Google Scholar 

  65. Riess, A.G., et al.: Astrophys. J. 659, 98 (2007)

    ADS  Google Scholar 

  66. Robertson, H.P.: Ann. Math. 496, 33 (1932)

    Google Scholar 

  67. Sahoo, P.K., Sivakumar, M.: Astrophys. Space Sci. 357(1), 60 (2015)

    ADS  Google Scholar 

  68. Sahoo, P.K., Tripathy, S.K., Sahoo, P.: Mod. Phys. Lett. A 33(33), 1850193 (2018)

    ADS  Google Scholar 

  69. Sciama, D.W.: Festschrift for Leopold Infeld. Pergamon, New York (1962)

    Google Scholar 

  70. Siamak, A., Qorani, E., Khajenabi, F.: Europhys. Lett. 119(2), 29002 (2017)

    ADS  Google Scholar 

  71. Spergel, D.N., et al.: Astrophys. J. Suppl. Ser. 148(1), 175 (2003)

    ADS  Google Scholar 

  72. Spergel, D.N., et al.: Astrophys. J. Suppl. Ser. 170(2), 377 (2007)

    ADS  Google Scholar 

  73. Taylor, P.L., et al.: Phys. Rev. D 98(2), 023522 (2018)

    MathSciNet  ADS  Google Scholar 

  74. Toporensky, A.V., Tretyakov, P.V.: Phys. Rev. D 102(4), 044049 (2020)

    MathSciNet  ADS  Google Scholar 

  75. Trautman, A.: Math. Astron. Phys. 20(185), 503 (1972)

    Google Scholar 

  76. Vignolo, S., Fabbri, L.: Int. J. Geom. Methods Mod. Phys. 9(07), 1250054 (2012)

    MathSciNet  Google Scholar 

  77. Visser, M.: Class. Quantum Gravity 21(11), 2603 (2004)

    ADS  Google Scholar 

  78. Wanas, M.I.: Symposium-International Astronomical Union, vol. 168. Cambridge University Press, Cambridge (1996)

    Google Scholar 

  79. Wanas, M.I.: Turk. J. Phys. 24(3), 473 (2000)

    Google Scholar 

  80. Wanas, M.I.: Int. J. Mod. Phys. A 22(31), 5709 (2007)

    MathSciNet  ADS  Google Scholar 

  81. 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)

    Google Scholar 

  82. Wanas, M.I.: ArXiv preprint (2010). 1006.2154

  83. Wanas, M.I., Bakry, M.A.: Int. J. Mod. Phys. A 24(27), 5025 (2009)

    ADS  Google Scholar 

  84. Wanas, M.I., Hassan, H.A.: Int. J. Theor. Phys. 53(11), 3901 (2014)

    Google Scholar 

  85. Wanas, M.I., Ammar, S.A., Refaey, S.A.: Can. J. Phys. 96(12), 1373 (2018a)

    ADS  Google Scholar 

  86. Wanas, M.I., Samah, A.A., Refaey, S.A.: Can. J. Phys. 96(12), 1373 (2018a)

    ADS  Google Scholar 

  87. Wanas, M.I., Kamal, M.M., Dabash, T.F.: Eur. Phys. J. Plus 133(1), 1 (2018b)

    Google Scholar 

  88. Wolfgang, H., Niemeyer, J.C.: Annu. Rev. Astron. Astrophys. 38(1), 191 (2000)

    Google Scholar 

  89. Xiao, K., Wang, S.Q.: Mod. Phys. Lett. A 35(35), 2050293 (2020)

    MathSciNet  ADS  Google Scholar 

  90. Yo, H.J., Nester, J.M.: Int. J. Mod. Phys. D 8(04), 459 (1999). https://doi.org/10.1142/S021827189900033X

    Article  ADS  Google Scholar 

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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.

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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.

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Correspondence to A. Eid.

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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

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Keywords

  • Absolute parallelism geometry
  • Field equations
  • Torsion
  • Shear
  • Big Rip cosmological models