Skip to main content
SpringerLink
Log in

Thermodynamics in Little Rip cosmology in the framework of a type of f(R, T) gravity

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract.

The cosmological reconstruction of the Little Rip model in f (R, T) gravity is investigated, where R is the curvature scalar and T the trace of the energy momentum tensor. The model perfectly reproduces the present stage of the universe, characterized by the \( \Lambda\) CDM model, without singularity at future finite-time (without the Big Rip). The input parameters are determined according to Supernovae cosmology data and perfectly fit with the WMAP around the Little Rip. Moreover, the thermodynamics is considered in this Little Rip cosmology and it is illustrated that the second law of thermodynamics is always satisfied around the Little Rip universe for the temperature inside the horizon being the same as that of the apparent horizon. Moreover, we show the existence of a stable fixed point in the Little Rip universe which confirms that this is actually a late-time attractor in the phantom-dominated universe. The linear perturbation analysis is performed around the critical points, showing that the Little Rip model obtained is stable.

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

Similar content being viewed by others

References

  1. T.M. Davis et al., Astrophys. J. 666, 716 (2007) arXiv:astro-ph/0701510

    Article  ADS  Google Scholar 

  2. WMAP Collaboration (Dunkley), Observations: arXiv:0803.0586 [astro-ph]

  3. WMAP Collaboration (E. Komatsu), arXiv:0803.0547 [astro-ph]

  4. T. Padmanabhan, AIP Conf. Proc. 861, 179 (2006) arXiv:astro-ph/0603114

    Article  ADS  Google Scholar 

  5. A.A. Starobinsky, Phys. Lett. B 91, 99 (1980)

    Article  ADS  Google Scholar 

  6. M.B. Mijic, M.S. Morris, W. Suen, Phys. Rev. D 34, 2934 (1986)

    Article  ADS  Google Scholar 

  7. P.A. Anderson, W. Suen, Phys. Rev. D 35, 2940 (1987)

    Article  ADS  Google Scholar 

  8. T.P. Sotiriou, V. Faraoni, Rev. Mod. Phys. 82, 451 (2010)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  9. A.G. Riess et al., Astron. J. 116, 1009 (1998)

    Article  ADS  Google Scholar 

  10. S. Perlmutter et al., Nature (London) 391, 51 (1998)

    Article  ADS  Google Scholar 

  11. P.M. Garnavich et al., Astrophys. J. 509, 74 (1998)

    Article  ADS  Google Scholar 

  12. S. Perlmutter et al., Astrophys. J. 517, 565 (1999)

    Article  ADS  Google Scholar 

  13. T. Harko, F.S.N. Lobo, S. Nojiri, S.D. Odintsov, Phys. Rev. D 84, 024020 (2011) arXiv:1104.2669 [gr-qc]

    Article  ADS  Google Scholar 

  14. M.J.S. Houndjo, Int. J. Mod. Phys. D 21, 1250003 (2012) arXiv:1107.3887 [astro-ph.CO]

    Article  ADS  MathSciNet  Google Scholar 

  15. M.J.S. Houndjo, O.F. Piattella, Int. J. Mod. Phys. D 21, 1250024 (2012) arXiv:1111.4275 [gr.qc]

    Article  ADS  Google Scholar 

  16. D. Momeni, M. Jamil, R. Myrzakulov, Eur. Phys. J. C 72, () arXiv:1107.5807 [physics.gen-ph]

  17. M.J.S. Houndjo, C.E.M. Batista, J.P. Campos, O.F. Piattella, Can. J. Phys. 91, 548 (2013) arXiv:1203.6084 [gr-qc]

    Article  Google Scholar 

  18. F.G. Alvarenga, M.J.S. Houndjo, A.V. Monwanou, Jean B. Chabi-Orou, J. Mod. Phys. 4, 130 (2013) arXiv:1205.4678 [gr-qc]

    Article  Google Scholar 

  19. P.H. Frampton, K.J. Ludwick, R.J. Sherrer, Phys. Rev. D 84, 063003 (2011)

    Article  ADS  Google Scholar 

  20. S. Nojiri, S.D. Odintsov, D. Saez-Gomez, Cyclic, ekpyrotic and little rip universe in modified gravity, arXiv:1108.0767 [hep-th]

  21. A.J. Lopez-Revelles, R. Myrzakulov, D. Saez-Gomez, Phys. Rev. D 85, 103521 (2012) arXiv:1201.5647 [gr-qc]

    Article  ADS  Google Scholar 

  22. Kazuharu Bamba, Salvatore Capozziello, Shin’ichi Nojiri, Sergei D. Odintsov, Astrophys. Space Sci. 342, 155 (2012) arXiv:1205.3421

    Article  ADS  Google Scholar 

  23. Paul H. Frampton, Kevin J. Ludwick, Shin’ichi Nojiri, Sergei D. Odintsov, Robert J. Scherrer, Phys. Lett. B 708, 204 (2012)

    Article  ADS  Google Scholar 

  24. Artyom V. Astashenok, Shin’ichi Nojiri, Sergei D. Odintsov, Artyom V. Yurov, Phys. Lett. B 709, 396 (2012) arXiv:1201.4056

    Article  ADS  Google Scholar 

  25. Yusaku Ito, Shin’ichi Nojiri, Sergei D. Odintsov, arXiv:1111.5389

  26. J.M. Bardeen, B. Carter, S.W. Hawking, Commun. Math. Phys. 31, 161 (1973)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  27. J.D. Bekenstein, Phys. Rev. D 7, 2333 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  28. S.W. Hawking, Commun. Math. Phys. 43, 199 (1975) 46

    Article  ADS  MathSciNet  Google Scholar 

  29. G.W. Gibbons, S.W. Hawking, Phys. Rev. D 15, 2738 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  30. T. Padmanabhan, arXiv:0910.0839 [gr-qc]

  31. T. Padmanabhan, AIP Conf. Proc. 1241, 93 (2010) arXiv:0911.1403 [gr-qc]

    Article  ADS  Google Scholar 

  32. T. Padmanabhan, Rep. Prog. Phys. 73, 046901 (2010)

    Article  ADS  Google Scholar 

  33. T. Jacobson, Phys. Rev. Lett. 75, 1260 (1995)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  34. E. Elizalde, P.J. Silva, Phys. Rev. D 78, 061501 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  35. K. Bamba, C.Q. Geng, S. Nojiri, S.D. Odintsov, EPL 89, 50003 (2010)

    Article  ADS  Google Scholar 

  36. S.F. Wu, B. Wang, X.H. Ge, G.H. Yang, Phys. Rev. D 81, 044010 (2010)

    Article  ADS  Google Scholar 

  37. Y. Yokokura, arXiv:1106.3149 [hep-th]

  38. R. Brustein, M. Hadad, Phys. Rev. Lett. 103, 101301 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  39. K. Bamba, R. Myrzakulov, S. Nojiri, S.D. Odintsov, Phys. Rev. D 85, 104036 (2012) arXiv:1202.4057v3 [physics.gen-ph]

    Article  ADS  Google Scholar 

  40. M. Hamani Daouda, Manuel E. Rodrigues, M.J.S. Houndjo, Eur. Phys. J. C 72, 1890 (2012) arXiv:1109.0528 [physics.gen-ph]

    Article  ADS  Google Scholar 

  41. Manuel E. Rodrigues, Zui A.A. Oporto, Phys. Rev. D 85, 104022 (2012) arXiv:1201.5337 [gr-qc]

    Article  ADS  Google Scholar 

  42. Manuel E. Rodrigues, Glauber T. Marques, Gen. Relativ. Gravit. 45, 1297 (2013) arXiv:1206:0763 [gr-qc]

    Article  ADS  MATH  MathSciNet  Google Scholar 

  43. Deborah F. Jardim, Manuel E. Rodrigues, Stephane J.M. Houndjo, Eur. Phys. J. Plus 127, 123 (2012) arXiv:1202.2830 [gr.qc]

    Article  Google Scholar 

  44. Manuel E. Rodrigues, Deborah F. Jardim, Stephane J.M. Houndjo, Gen. Relativ. Gravit. 45, 2309 (2013) arXiv:1205.3481 [gr-qc]

    Article  ADS  MATH  MathSciNet  Google Scholar 

  45. Paul H. Frampton, Kevin J. Ludwick, Robert J. Scherrer, Phys. Rev. D 84, 063003 (2011) arXiv:1106.4996 [astro-ph.CO]

    Article  ADS  Google Scholar 

  46. I. Brevik, E. Elizalde, S. Nojiri, S.D. Odintsov, Phys. Rev. D 84, 103508 (2011) arXiv:1107.4642 [hep-th]

    Article  ADS  Google Scholar 

  47. Makarenko Andrey N., Obukhov Valery V., Kirnos IIya V, From Big to Little Rip in modified $f(R,G)$ gravity, arXiv:1201.4742 [gr-qc]

  48. S. Capozziello, M. De Laurentis, S. Nojiri, S.D. Odintsov, Phys. Rev. D 79, 124007 (2009) arXiv:0903.2753v2 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  49. E.W. Kolb, M.S. Turner, The Early Universe (Addison-Wesley, Redwood City, California, 1990)

  50. WMAP Collaboration (E. Komatsu et al.), Astrophys. J. Suppl. 192, 18 (2011) arXiv:1001.4538 [astro-ph.CO]

    Article  ADS  Google Scholar 

  51. R. Amanullah et al., Astrophys. J. 716, 712 (2010)

    Article  ADS  Google Scholar 

  52. N.J. Poplawski, arXiv:gr-qc/0608031v2

  53. M.S. Berman, Phys. Rev. D 43, 1075 (1991) M. Bronstein, Phys. Z. Sowjetunion 3

    Article  ADS  Google Scholar 

  54. G. Magnano, gr-qc/9511027 (1995)

  55. K. Bamba, C.Q. Geng, JCAP 11, 008 (2011) arXiv:1109.1694 [gr-qc]

    Article  ADS  Google Scholar 

  56. K. Bamba, C.Q. Geng, JCAP 06, 014 (2010) arXiv:1005.5234 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  57. T. Jacobson, Phys. Rev. Lett. 75, 1260 (1995) arXiv:gr-qc/9504004

    Article  ADS  MATH  MathSciNet  Google Scholar 

  58. C. Eling, R. Guedens, T. Jacobson, Phys. Rev. Lett. 96, 121301 (2006) arXiv:gr-qc/0602001

    Article  ADS  MathSciNet  Google Scholar 

  59. E. Elizalde, P.J. Silva, Phys. Rev. D 78, 061501 (2008) arXiv:0804.3721 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  60. K. Bamba, C.Q. Geng, S. Nojiri, S.D. Odintsov, EPL 89, 50003 (2010) arXiv:0909.4397 [hep-th]

    Article  ADS  Google Scholar 

  61. S.F. Wu, B. Wang, X.H. Ge, G.H. Yang, Phys. Rev. D 81, 044010 (2010) arXiv:0909.1367 [gr-qc]

    Article  ADS  Google Scholar 

  62. Y. Yokokura, arXiv:1106.3149 [hep-th]

  63. R. Brustein, M. Hadad, Phys. Rev. Lett. 103, 101301 (2009) arXiv:0903.0823 [hep-th]

    Article  ADS  MathSciNet  Google Scholar 

  64. R. Brustein, A.J.M. Medved, arXiv:1201.5754 [hep-th]

  65. J. Zhou, B. Wang, Y. Gong, E. Abdalla, Phys. Lett. B 652, 86 (2007)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  66. R. Brustein, D. Gorbonos, M. Hadad, Phys. Rev. D 79, 044025 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  67. J.M. Bardeen, B. Carter, S.W. Hawking, Commun. Math. Phys. 31, 161 (1973)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  68. J.D. Bekenstein, Phys. Rev. D 7, 2333 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  69. R.G. Cai, S.P. Kim, JHEP 02, 050 (2005) arXiv:hep-th/0501055

    Article  ADS  MathSciNet  Google Scholar 

  70. S.A. Hayward, Class. Quantum. Grav. 15, 3147 (1998) arXiv:gr-qc/9710089

    Article  ADS  MATH  MathSciNet  Google Scholar 

  71. S.A. Hayward, S. Mukohyama, M.C. Ashworth, Phys. Lett. A 256, 347 (1999) arXiv:gr-qc/9810006

    Article  ADS  MathSciNet  Google Scholar 

  72. R.G. Cai, L.M. Cao, Phys. Rev. D 75, 064008 (2007) arXiv:gr-qc/0611071

    Article  ADS  MathSciNet  Google Scholar 

  73. Kazuharu Bamba, Chao-Qiang Geng, arXiv:1109.1694v2 [gr-qc]

  74. M. Sharif, M. Zubair, JCAP 03, 028 (2012) arXiv:1204.0848v2 [gr-qc]

    Article  ADS  Google Scholar 

  75. H. Mohseni Sadjadi, Phys. Scri. 05, 055006 (2011) arXiv:1009.1839v2 [gr-qc]

    Article  ADS  Google Scholar 

  76. H. Mohseni Sadjadi, Phys. Rev. D 73, 063525 (2006)

    Article  ADS  Google Scholar 

  77. A. Aviles, A. Bravett, S. Capozziello, O. Luongo, Phys. Rev. D 87, 044012 (2013) arXiv:1210.5149v2 [gr-qc]

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Engenharia e Ciências Naturais - CEUNES - Universidade Federal do Espírito Santo, CEP 29933-415, São Mateus/ES, Brazil

    M. J. S. Houndjo & F. G. Alvarenga

  2. Institut de Mathématiques et de Sciences Physiques (IMSP), 01 BP 613, Porto-Novo, Benin

    M. J. S. Houndjo

  3. Universidade Federal do Espírito Santo - Centro de Ciências Exatas - Departamento de Física, Av. Fernando Ferrari s/n, CEP29075-910, Vitória/ES, Brazil

    Manuel E. Rodrigues

  4. Faculdade de Ciências Exatas e Tecnologia, Universidade Federal do Pará, Campus Universitário de Abaetetuba, CEP 68440-000, Abaetetuba, Brazil

    Manuel E. Rodrigues

  5. Universidade Federal dos Vales do Jequitinhonha e Mucuri, ICTM, Rua do Cruzeiro, 01, Jardim São Paulo, CEP39803-371, Teofilo Otoni, MG, Brazil

    Deborah F. Jardim

  6. Eurasian International Center for Theoretical Physics, L.N. Gumilyov Eurasian National University, 010008, Astana, Kazakhstan

    R. Myrzakulov

Authors
  1. M. J. S. Houndjo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. G. Alvarenga
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Manuel E. Rodrigues
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Deborah F. Jardim
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. R. Myrzakulov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. J. S. Houndjo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Houndjo, M.J.S., Alvarenga, F.G., Rodrigues, M. et al. Thermodynamics in Little Rip cosmology in the framework of a type of f(R, T) gravity. Eur. Phys. J. Plus 129, 171 (2014). https://doi.org/10.1140/epjp/i2014-14171-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2014-14171-6

Keywords

Search

Navigation