Skip to main content
SpringerLink
Log in

Big Rip and Big Crunch Cosmological Models in a Gravitational Field with Torsion

  • Published:
Gravitation and Cosmology Aims and scope Submit manuscript

Abstract

The gravitational field with torsion is being constructed by using the parametrized absolute parallelism geometry. A generalized law of variation of Hubble’s parameter in evolutionary cosmological models is used. The cosmological models under the influence of the gravitational field with torsion are obtained and discussed. A new model of the Universe is presented using a special class of Riemann–Cartan geometry. This model is oscillating with expansion and contraction at different stages. It behaves normally as the conventional Big Bang model in the first half-age until it reaches the moment of a Big Rip, then reverses its behavior as a result of a changes in the pressure and torsion until it reaches a Big Crunch at the end of the second half-age. We suppose that the Big Rip singularity is replaced by a regular maximum of the scale factor at the Big Rip due to a possible physical mechanism of quantum nature. The positivity condition for the energy density of matter leads to exclusion of open and closed universes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

REFERENCES

  1. E. Sezgin and P. Van Nieuwenhuizen, “Renormalizability properties of antisymmetric tensor fields coupled to gravity,” Phys. Rev. D 22 (2), 301(1980).

    Article  ADS  MathSciNet  Google Scholar 

  2. F. W. Hehl, J. D. McCrea, E. W. Mielke, and Y. Ne’eman, “Metric-affine gauge theory of gravity: field equations, Noether identities, world spinors, and breaking of dilation invariance,” Phys. Rep. 258 (1-2), 1 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  3. I. L. Shapiro, “Physical aspects of the space–time torsion,” Phys. Rep. 357 (2), 113 (2002).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. T. R. Hammond, “Torsion gravity,” Rep. Prog. Phys. 65 (5), 599 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  5. I. B. Khriplovich and A. A. Pomeransky, “Immirzi parameter, torsion, and discrete symmetries,” Phys. Rev. D 73 (10), 107502 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  6. N. Dragon, “Torsion and curvature in extended supergravity,” Z. Phys. C 2 (1), 29 (1979).

    Article  ADS  MathSciNet  Google Scholar 

  7. W. E. Mielke and E. S. Romero, “Cosmological evolution of a torsion-induced quintaxion,” Phys. Rev.D73 (4), 043521 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  8. M. A. Zubkov, “Torsion instead of Technicolor,” Mod. Phys. Lett. A 25 (34), 2885 (2010).

    Article  ADS  MATH  Google Scholar 

  9. P. Baekler and W. Friedrich, “Beyond Einstein–Cartan gravity: quadratic torsion and curvature invariants with even and odd parity including all boundary terms,” Class. Quantum Grav. 28 (21), 215017 (2011).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. U. Seljak, A. Makarov, P. McDonald, S. F. Anderson, N. A. Bahcall, et al., “Cosmological parameter analysis including SDSS Ly \(\alpha\) forest and galaxy bias: constraints on the primordial spectrum of fluctuations, neutrino mass, and dark energy,” Phys. Rev. D 71 (10), 103515 (2005).

    Article  ADS  Google Scholar 

  11. M. S. Carroll, H. William, and T. Edwin, “The cosmological constant,” Ann. Rev. Astron. Astrophys. 30 (1), 499 (1992).

    Article  ADS  Google Scholar 

  12. T. Padmanabhan, “Cosmological constant—the weight of the vacuum,” Phys. Rep. 380 (5–6), 235 (2003).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. M. Will, “The confrontation between general relativity and experiment,” Living Rev. Rel. 9 (1), 3 (2006).

    Article  MATH  Google Scholar 

  14. F. W. Hehl, P. V. Heyde, G. D. Kerlick, and J. M. Nester, “General relativity with spin and torsion: Foundations and prospects,” Rev. Mod. Phys. 48 (3), 393 (1976).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. S. Capozziello, G. Lambiase, and C. Stornaiolo, “Geometric classification of the torsion tensor of space-time,” Ann. der Phys. 10 (8), 713 (2001).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. M. Gasperini, “Repulsive gravity in the very early universe,” Gen. Rel. Grav. 30 (12), 1703 (1998).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. M. Szydłowski and A. Krawiec, “Cosmological model with macroscopic spin fluid,” Phys. Rev. D 70 (4), 043510 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  18. E. Cartan, “Sur les variétés à connexion affine et la théorie de la relativité généralisée (première partie),” Ann. Sci. Éc. Normale supér 40, 325 (1923).

    Article  MathSciNet  MATH  Google Scholar 

  19. D. W. Sciama, “On the analog between charge and spin in General Relativity,” in Recent Developments in General Relativity, Festschrift for Leopold Infeld, (Pergamon Press, New York, 1962).

    Google Scholar 

  20. T. W. Kibble, “Lorentz invariance and the gravitational field,” J. Mat. Phys. 2 (2), 212 (1961).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. A. Trautmann, Bull. Acad. Pol. Sci., Ser. Sci., Math., Astron. Phys. 20, 895 (1972).

    Google Scholar 

  22. M. I. Wanas, “Motion of spinning particles in gravitational fields,” Astrophys. Space Sci. 258 (1-2), 237 (1997).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. M. I. Wanas, “Parameterized absolute parallelism: a geometry for physical applications,” Turk. J. Phys. 24 (3), 473 (2000).

    Google Scholar 

  24. V. C. De Andrade and J. G. Pereira, “Riemannian and teleparallel descriptions of the scalar field gravitational interaction,” Gen. Rel. Grav. 30, 263 (1998).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. M. I.Wanas, “The other side of gravity and geometry: antigravity and anticurvature,” Adv. High Ener. Phys. (2012).

    MATH  Google Scholar 

  26. C. Brans and R. Dicke, “Mach’s principle and a relativistic theory of gravitation,” Phys. Rev. 124 (3), 925 (1961).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. S. Weinberg, Gravitation and Cosmology (John Wiley and Sons, New York, 1972).

    Google Scholar 

  28. H. P. Robertson, “Groups of motions in spaces admitting absolute parallelism,” Ann. Math. 496 (1932).

  29. M. S. Berman, “A special law of variation for Hubble’s parameter,” Nuovo Cim. B 74 (2), 182 (1983).

    Article  ADS  Google Scholar 

  30. M. S. Berman and Fernando de Mello Gomide, “Cosmological models with constant deceleration parameter,” Gen. Rel. Grav. 20 (2), 191 (1988).

    Article  ADS  Google Scholar 

  31. Ö. Akarsu and D. Tekin, “Cosmological models with linearly varying deceleration parameter,” Int. J. Theor. Phys. 51 (2), 612 (2012).

    Article  MATH  Google Scholar 

  32. P. De Bernardis, P. A. Ade, J. J. Bock, J. R. Bond, J. Borrill, A. Boscaleri, and P. G. Ferreira, “A flat Universe from high-resolution maps of the cosmic microwave background radiation,” Nature 404 (6781), 955 (2000).

    Article  ADS  Google Scholar 

  33. A. B. Lahanas, V. C. Spanos, and D. V. Nanopoulos, “Neutralino dark matter elastic scattering in a flat and accelerating universe,” Mod. Phys. Lett. A 16 (19), 1229 (2001).

    Article  ADS  Google Scholar 

  34. M. I. Wanas and M. A. Bakry, “Effect of spin–torsion interaction on Raychaudhuri equations,” Int. Mod. Phys. A 24 (27), 5025 (2009).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  35. M. I. Wanas, M. M. Kamal, and T. F. Dabash, “Initial singularity and pure geometric field theories,” Eur. Phys. J. Plus 133 (1), 21 (2018).

    Article  Google Scholar 

  36. R. T. Hammond, “Torsion gravity,” Rep. Prog. Phys. 65 (5), 599 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  37. Y. Mao, M. Tegmark, A. H. Guth, and S. Cabi, “Constraining torsion with gravity probe B,” Phys. Rev. D 76 (10), 104029 (2007).

    Article  ADS  Google Scholar 

  38. A. V. Kostelecký, N. Russell, and J. D. Tasson, “Constraints on torsion from bounds on Lorentz violation,” Phys. Rev. Lett. 100 (11), 111102 (2008).

    Article  ADS  Google Scholar 

  39. R. March, G. Bellettini, R. Tauraso, and S. Dell’Angello, “Constraining spacetime torsion with the Moon and Mercury,” Phys. Rev. D 83 (10), 104008 (2011).

    Article  ADS  Google Scholar 

  40. F. W. Hehl, Y. N. Obukhov, and D. Puetzfeld, “On Poincaré gauge theory of gravity, its equations of motion, and Gravity Probe B,” Phys. Lett. A 377 (31-33), 1775 (2013).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. D. Puetzfeld and Y. N. Obukhov, “Prospects of detecting spacetime torsion,” Int. J. Mod. Phys. D 23 (12), 1442004 (2014).

    Article  ADS  MATH  Google Scholar 

  42. H. Lin, X. H. Zhai, and X. Z. Li, “Solar system tests for realistic f (T) models with non-minimal torsion–matter coupling,” Eur. Phys. J. C 77 (8), 504 (2017).

    Article  ADS  Google Scholar 

  43. M. I. Wanas and H. A. Hassan, “Torsion and particle horizons,” Int. J. Theor. Phys. 53 (11), 3901 (2014).

    Article  MATH  Google Scholar 

  44. S. M. Carroll, M. Hoffman, and M. Trodden, “Can the dark energy equation-of-state parameter w be less than -1?,” Phys. Rev. D 68, 023509 (2003).

    Article  ADS  Google Scholar 

  45. R. R. Caldwell, M. Kamionkowski and N. N. Weinberg, “Phantom energy: dark energy with \(w<{-}1\) causes a cosmic doomsday,” Phys. Rev. Lett. 91, 071301 (2003).

    Article  ADS  Google Scholar 

  46. R. T. Hammond, “Geometrization of string theory gravity,” Gen. Rel. Grav. 30 (12), 1803 (1998).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. R. T. Hammond, “Helicity flip cross section from gravity with torsion,” Class. Quantum Grav. 13 (7), 1691 (1996).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. F. W. Hehl, P. V. Heyde, and G. D. Kerlick, “General relativity with spin and torsion and its deviations from Einstein’s theory,” Phys. Rev. D 10 (4), 1066 (1974).

    Article  ADS  MathSciNet  Google Scholar 

  49. J. V. Cunha and J. A. S. Lima, “Transition redshift: new kinematic constraints from supernovae,” Mon. Not. Roy. Astron. Soc. 390 (1), 210 (2008).

    Article  ADS  Google Scholar 

  50. S. Perlmutter, S. Gabi, G. Goldhaber, A. Goobar, D. E. Groom, et al., “Measurements of the cosmological parameters \(\Omega\) and \(\Lambda\) from the first seven Supernovae at \(z\geq 0.35\),” Astrophys. J. 483 (2), 565 (1997).

    Article  ADS  Google Scholar 

  51. S. Perlmutter, G. Aldering, M. Della Valle, S. Deustua, R. S. Ellis, et al., “Discovery of a supernova explosion at half the age of the Universe,” Nature 391 (6662), 51 (1998).

    Article  ADS  Google Scholar 

  52. S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, P. Nugent, et al., “Measurements of \(\Omega\) and \(\Lambda\) from 42 high-redshift Supernovae,” Astrophys. J. 517 (1999).

  53. A. G. Riess, L.-G. Strolger, J. Tonry, S. Casertano, H. C. Ferguson, et al., “Type Ia supernova discoveries at \(z>1\) from the Hubble Space Telescope: Evidence for past deceleration and constraints on dark energy evolution,” Astrophys. J. 607 (2), 665 (2004).

    Article  ADS  MATH  Google Scholar 

  54. D. J. Eisenstein, I. Zehavi, D. W. Hogg, R. Scoccimarro, M. R. Blanton, et al., “Detection of the baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies,” Astrophys J. 633 (2), 560 (2005).

    Article  ADS  Google Scholar 

  55. A. A. Starobinsky, “Stochastic de Sitter (inflationary) stage in the early universe,” in: Field Theory, Quantum Gravity and Strings, 107 (Springer, Berlin, Heidelberg, 1988).

    Google Scholar 

  56. T. Gonzalez, R. Cardenas, Y. Leyva, O. Martin, and I. Quiros, “Predictions for Supernovae type IA observations,” 297, (2003).

  57. M. S. Turner, “Dark matter and dark energy: the critical questions,“ astro-ph/0207297.

  58. P. Peebles and B. Ratra, “The cosmological constant and dark energy,” Rev. Mod. Phys. 75 (2).559 (2003).

  59. T. Padmanabhan, “Cosmological constant—the weight of the vacuum,” Phys. Rep. 380 (5–6), 235 (2003).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  60. P. Astier, J. Guy, N. Regnault, R. Pain, E. Aubourg, et al., “The Supernova Legacy Survey: measurement of \(q\) and \(w\) from the first year data set,” Astron. Astrophys. 447 (1), 31 (2006).

    Article  ADS  Google Scholar 

  61. E. Komatsu, K. M. Smith, and J. Dunkley, “Seven-year WMAP observations: Cosmological interpretation,” arXiv: 1001.4538.

  62. S. M. Berman, “Static universe in a modified Brans-Dicke cosmology,” Int. J. Theor. Phys. 29 (6), 567 (1990).

    Article  MATH  Google Scholar 

  63. S. M. Berman, “Cosmological models with variable gravitational and cosmological ‘constants’,” Gen. Rel. Grav. 23 (4), 465 (1991).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  64. S. D. Maharaj and R. Naidoo, “Solutions to the field equations and the deceleration parameter,” Astroph. Sp. Sci. 208 (2), 261 (1993).

    Article  ADS  MATH  Google Scholar 

  65. M. A. Bakry and A. T. Shafeek, “The periodic universe with varying deceleration parameter of the second degree,” Astroph. Space Sci. 364,135 (2019).

    Article  ADS  MathSciNet  Google Scholar 

Download references

ACKNOWLEDGMENT

We would like to express my sincere thanks and appreciation to the reviewers for their insightful comments and constructive suggestions leading to much improvement in the current form of the paper. Additionally, much appreciate to Prof. M. I. Wanas (Cairo University, Egypt) for his deepest interest and useful feedback.

Author information

Authors and Affiliations

  1. Mathematics Department, Faculty of Education, Ain Shams University, Cairo, Egypt

    M. A. Bakry & Aryn T. Shafeek

Authors
  1. M. A. Bakry
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aryn T. Shafeek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to M. A. Bakry or Aryn T. Shafeek.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bakry, M.A., Shafeek, A.T. Big Rip and Big Crunch Cosmological Models in a Gravitational Field with Torsion. Gravit. Cosmol. 27, 89–104 (2021). https://doi.org/10.1134/S0202289321010047

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0202289321010047

Search

Navigation