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

  • M. J. S. Houndjo
  • F. G. Alvarenga
  • Manuel E. Rodrigues
  • Deborah F. Jardim
  • R. Myrzakulov
Regular Article

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.

Keywords

Dark Energy Hubble Parameter Apparent Horizon Energy Momentum Tensor Gravitational Action 

References

  1. 1.
    T.M. Davis et al., Astrophys. J. 666, 716 (2007) arXiv:astro-ph/0701510 ADSCrossRefGoogle Scholar
  2. 2.
    WMAP Collaboration (Dunkley), Observations: arXiv:0803.0586 [astro-ph]
  3. 3.
    WMAP Collaboration (E. Komatsu), arXiv:0803.0547 [astro-ph]
  4. 4.
    T. Padmanabhan, AIP Conf. Proc. 861, 179 (2006) arXiv:astro-ph/0603114 ADSCrossRefGoogle Scholar
  5. 5.
    A.A. Starobinsky, Phys. Lett. B 91, 99 (1980)ADSCrossRefGoogle Scholar
  6. 6.
    M.B. Mijic, M.S. Morris, W. Suen, Phys. Rev. D 34, 2934 (1986)ADSCrossRefGoogle Scholar
  7. 7.
    P.A. Anderson, W. Suen, Phys. Rev. D 35, 2940 (1987)ADSCrossRefGoogle Scholar
  8. 8.
    T.P. Sotiriou, V. Faraoni, Rev. Mod. Phys. 82, 451 (2010)ADSMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    A.G. Riess et al., Astron. J. 116, 1009 (1998)ADSCrossRefGoogle Scholar
  10. 10.
    S. Perlmutter et al., Nature (London) 391, 51 (1998)ADSCrossRefGoogle Scholar
  11. 11.
    P.M. Garnavich et al., Astrophys. J. 509, 74 (1998)ADSCrossRefGoogle Scholar
  12. 12.
    S. Perlmutter et al., Astrophys. J. 517, 565 (1999)ADSCrossRefGoogle Scholar
  13. 13.
    T. Harko, F.S.N. Lobo, S. Nojiri, S.D. Odintsov, Phys. Rev. D 84, 024020 (2011) arXiv:1104.2669 [gr-qc]ADSCrossRefGoogle Scholar
  14. 14.
    M.J.S. Houndjo, Int. J. Mod. Phys. D 21, 1250003 (2012) arXiv:1107.3887 [astro-ph.CO]ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    M.J.S. Houndjo, O.F. Piattella, Int. J. Mod. Phys. D 21, 1250024 (2012) arXiv:1111.4275 [gr.qc]ADSCrossRefGoogle Scholar
  16. 16.
    D. Momeni, M. Jamil, R. Myrzakulov, Eur. Phys. J. C 72, () arXiv:1107.5807 [physics.gen-ph]
  17. 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]CrossRefGoogle Scholar
  18. 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]CrossRefGoogle Scholar
  19. 19.
    P.H. Frampton, K.J. Ludwick, R.J. Sherrer, Phys. Rev. D 84, 063003 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    S. Nojiri, S.D. Odintsov, D. Saez-Gomez, Cyclic, ekpyrotic and little rip universe in modified gravity, arXiv:1108.0767 [hep-th]
  21. 21.
    A.J. Lopez-Revelles, R. Myrzakulov, D. Saez-Gomez, Phys. Rev. D 85, 103521 (2012) arXiv:1201.5647 [gr-qc]ADSCrossRefGoogle Scholar
  22. 22.
    Kazuharu Bamba, Salvatore Capozziello, Shin’ichi Nojiri, Sergei D. Odintsov, Astrophys. Space Sci. 342, 155 (2012) arXiv:1205.3421 ADSCrossRefGoogle Scholar
  23. 23.
    Paul H. Frampton, Kevin J. Ludwick, Shin’ichi Nojiri, Sergei D. Odintsov, Robert J. Scherrer, Phys. Lett. B 708, 204 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    Artyom V. Astashenok, Shin’ichi Nojiri, Sergei D. Odintsov, Artyom V. Yurov, Phys. Lett. B 709, 396 (2012) arXiv:1201.4056 ADSCrossRefGoogle Scholar
  25. 25.
    Yusaku Ito, Shin’ichi Nojiri, Sergei D. Odintsov, arXiv:1111.5389
  26. 26.
    J.M. Bardeen, B. Carter, S.W. Hawking, Commun. Math. Phys. 31, 161 (1973)ADSMATHMathSciNetCrossRefGoogle Scholar
  27. 27.
    J.D. Bekenstein, Phys. Rev. D 7, 2333 (1973)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    S.W. Hawking, Commun. Math. Phys. 43, 199 (1975) 46ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    G.W. Gibbons, S.W. Hawking, Phys. Rev. D 15, 2738 (1977)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    T. Padmanabhan, arXiv:0910.0839 [gr-qc]
  31. 31.
    T. Padmanabhan, AIP Conf. Proc. 1241, 93 (2010) arXiv:0911.1403 [gr-qc]ADSCrossRefGoogle Scholar
  32. 32.
    T. Padmanabhan, Rep. Prog. Phys. 73, 046901 (2010)ADSCrossRefGoogle Scholar
  33. 33.
    T. Jacobson, Phys. Rev. Lett. 75, 1260 (1995)ADSMATHMathSciNetCrossRefGoogle Scholar
  34. 34.
    E. Elizalde, P.J. Silva, Phys. Rev. D 78, 061501 (2008)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    K. Bamba, C.Q. Geng, S. Nojiri, S.D. Odintsov, EPL 89, 50003 (2010)ADSCrossRefGoogle Scholar
  36. 36.
    S.F. Wu, B. Wang, X.H. Ge, G.H. Yang, Phys. Rev. D 81, 044010 (2010)ADSCrossRefGoogle Scholar
  37. 37.
    Y. Yokokura, arXiv:1106.3149 [hep-th]
  38. 38.
    R. Brustein, M. Hadad, Phys. Rev. Lett. 103, 101301 (2009)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    K. Bamba, R. Myrzakulov, S. Nojiri, S.D. Odintsov, Phys. Rev. D 85, 104036 (2012) arXiv:1202.4057v3 [physics.gen-ph]ADSCrossRefGoogle Scholar
  40. 40.
    M. Hamani Daouda, Manuel E. Rodrigues, M.J.S. Houndjo, Eur. Phys. J. C 72, 1890 (2012) arXiv:1109.0528 [physics.gen-ph]ADSCrossRefGoogle Scholar
  41. 41.
    Manuel E. Rodrigues, Zui A.A. Oporto, Phys. Rev. D 85, 104022 (2012) arXiv:1201.5337 [gr-qc]ADSCrossRefGoogle Scholar
  42. 42.
    Manuel E. Rodrigues, Glauber T. Marques, Gen. Relativ. Gravit. 45, 1297 (2013) arXiv:1206:0763 [gr-qc]ADSMATHMathSciNetCrossRefGoogle Scholar
  43. 43.
    Deborah F. Jardim, Manuel E. Rodrigues, Stephane J.M. Houndjo, Eur. Phys. J. Plus 127, 123 (2012) arXiv:1202.2830 [gr.qc]CrossRefGoogle Scholar
  44. 44.
    Manuel E. Rodrigues, Deborah F. Jardim, Stephane J.M. Houndjo, Gen. Relativ. Gravit. 45, 2309 (2013) arXiv:1205.3481 [gr-qc]ADSMATHMathSciNetCrossRefGoogle Scholar
  45. 45.
    Paul H. Frampton, Kevin J. Ludwick, Robert J. Scherrer, Phys. Rev. D 84, 063003 (2011) arXiv:1106.4996 [astro-ph.CO]ADSCrossRefGoogle Scholar
  46. 46.
    I. Brevik, E. Elizalde, S. Nojiri, S.D. Odintsov, Phys. Rev. D 84, 103508 (2011) arXiv:1107.4642 [hep-th]ADSCrossRefGoogle Scholar
  47. 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. 48.
    S. Capozziello, M. De Laurentis, S. Nojiri, S.D. Odintsov, Phys. Rev. D 79, 124007 (2009) arXiv:0903.2753v2 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  49. 49.
    E.W. Kolb, M.S. Turner, The Early Universe (Addison-Wesley, Redwood City, California, 1990)Google Scholar
  50. 50.
    WMAP Collaboration (E. Komatsu et al.), Astrophys. J. Suppl. 192, 18 (2011) arXiv:1001.4538 [astro-ph.CO]ADSCrossRefGoogle Scholar
  51. 51.
    R. Amanullah et al., Astrophys. J. 716, 712 (2010)ADSCrossRefGoogle Scholar
  52. 52.
    N.J. Poplawski, arXiv:gr-qc/0608031v2
  53. 53.
    M.S. Berman, Phys. Rev. D 43, 1075 (1991) M. Bronstein, Phys. Z. Sowjetunion 3ADSCrossRefGoogle Scholar
  54. 54.
    G. Magnano, gr-qc/9511027 (1995)Google Scholar
  55. 55.
    K. Bamba, C.Q. Geng, JCAP 11, 008 (2011) arXiv:1109.1694 [gr-qc]ADSCrossRefGoogle Scholar
  56. 56.
    K. Bamba, C.Q. Geng, JCAP 06, 014 (2010) arXiv:1005.5234 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  57. 57.
    T. Jacobson, Phys. Rev. Lett. 75, 1260 (1995) arXiv:gr-qc/9504004 ADSMATHMathSciNetCrossRefGoogle Scholar
  58. 58.
    C. Eling, R. Guedens, T. Jacobson, Phys. Rev. Lett. 96, 121301 (2006) arXiv:gr-qc/0602001 ADSMathSciNetCrossRefGoogle Scholar
  59. 59.
    E. Elizalde, P.J. Silva, Phys. Rev. D 78, 061501 (2008) arXiv:0804.3721 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  60. 60.
    K. Bamba, C.Q. Geng, S. Nojiri, S.D. Odintsov, EPL 89, 50003 (2010) arXiv:0909.4397 [hep-th]ADSCrossRefGoogle Scholar
  61. 61.
    S.F. Wu, B. Wang, X.H. Ge, G.H. Yang, Phys. Rev. D 81, 044010 (2010) arXiv:0909.1367 [gr-qc]ADSCrossRefGoogle Scholar
  62. 62.
    Y. Yokokura, arXiv:1106.3149 [hep-th]
  63. 63.
    R. Brustein, M. Hadad, Phys. Rev. Lett. 103, 101301 (2009) arXiv:0903.0823 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  64. 64.
    R. Brustein, A.J.M. Medved, arXiv:1201.5754 [hep-th]
  65. 65.
    J. Zhou, B. Wang, Y. Gong, E. Abdalla, Phys. Lett. B 652, 86 (2007)ADSMATHMathSciNetCrossRefGoogle Scholar
  66. 66.
    R. Brustein, D. Gorbonos, M. Hadad, Phys. Rev. D 79, 044025 (2009)ADSMathSciNetCrossRefGoogle Scholar
  67. 67.
    J.M. Bardeen, B. Carter, S.W. Hawking, Commun. Math. Phys. 31, 161 (1973)ADSMATHMathSciNetCrossRefGoogle Scholar
  68. 68.
    J.D. Bekenstein, Phys. Rev. D 7, 2333 (1973)ADSMathSciNetCrossRefGoogle Scholar
  69. 69.
    R.G. Cai, S.P. Kim, JHEP 02, 050 (2005) arXiv:hep-th/0501055 ADSMathSciNetCrossRefGoogle Scholar
  70. 70.
    S.A. Hayward, Class. Quantum. Grav. 15, 3147 (1998) arXiv:gr-qc/9710089 ADSMATHMathSciNetCrossRefGoogle Scholar
  71. 71.
    S.A. Hayward, S. Mukohyama, M.C. Ashworth, Phys. Lett. A 256, 347 (1999) arXiv:gr-qc/9810006 ADSMathSciNetCrossRefGoogle Scholar
  72. 72.
    R.G. Cai, L.M. Cao, Phys. Rev. D 75, 064008 (2007) arXiv:gr-qc/0611071 ADSMathSciNetCrossRefGoogle Scholar
  73. 73.
    Kazuharu Bamba, Chao-Qiang Geng, arXiv:1109.1694v2 [gr-qc]
  74. 74.
    M. Sharif, M. Zubair, JCAP 03, 028 (2012) arXiv:1204.0848v2 [gr-qc]ADSCrossRefGoogle Scholar
  75. 75.
    H. Mohseni Sadjadi, Phys. Scri. 05, 055006 (2011) arXiv:1009.1839v2 [gr-qc]ADSCrossRefGoogle Scholar
  76. 76.
    H. Mohseni Sadjadi, Phys. Rev. D 73, 063525 (2006)ADSCrossRefGoogle Scholar
  77. 77.
    A. Aviles, A. Bravett, S. Capozziello, O. Luongo, Phys. Rev. D 87, 044012 (2013) arXiv:1210.5149v2 [gr-qc]ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • M. J. S. Houndjo
    • 1
    • 2
  • F. G. Alvarenga
    • 1
  • Manuel E. Rodrigues
    • 3
    • 4
  • Deborah F. Jardim
    • 5
  • R. Myrzakulov
    • 6
  1. 1.Departamento de Engenharia e Ciências Naturais - CEUNES - Universidade Federal do Espírito SantoSão Mateus/ESBrazil
  2. 2.Institut de Mathématiques et de Sciences Physiques (IMSP)Porto-NovoBenin
  3. 3.Universidade Federal do Espírito Santo - Centro de Ciências Exatas - Departamento de FísicaVitória/ESBrazil
  4. 4.Faculdade de Ciências Exatas e TecnologiaUniversidade Federal do ParáAbaetetubaBrazil
  5. 5.Universidade Federal dos Vales do Jequitinhonha e Mucuri, ICTMTeofilo Otoni, MGBrazil
  6. 6.Eurasian International Center for Theoretical PhysicsL.N. Gumilyov Eurasian National UniversityAstanaKazakhstan

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