Thermodynamics in f (T) gravity and corrected entropies

Regular Article

Abstract

This paper is devoted to studying the generalized second law of thermodynamics in f (T) gravity. We use quantum corrections such as power law and logarithmic corrected entropies to the horizon entropy along with Gibbs’ equation in the thermal equilibrium state. We derive the f (T) model by taking into account a power law scale factor through the first modified Friedmann equation which obeys the condition for a realistic model. Two types of horizons, i.e. Hubble and event horizons, are used to check the validity of the generalized second law of thermodynamics with corrected entropies. We conclude that this law holds with a specific range of entropy parameter on both horizons in the case of power law corrected entropy, while it violates for all values of entropy parameter on both horizons for logarithmic corrected entropy.

References

  1. 1.
    R. Ferraro, F. Fiorini, Phys. Rev. D 75, 084031 (2007)ADSCrossRefMathSciNetGoogle Scholar
  2. 2.
    G.R. Bengochea, R. Ferraro, Phys. Rev. D 79, 124019 (2009)ADSCrossRefGoogle Scholar
  3. 3.
    E.V. Linder, Phys. Rev. D 81, 127301 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    J.W. Maluf, J. Math. Phys. 35, 335 (1994)ADSCrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    V.C. de Andrade, J.G. Pereira, Phys. Rev. D 56, 4689 (1997)ADSCrossRefMathSciNetGoogle Scholar
  6. 6.
    G.G.L. Nashed, Gen. Relativ. Gravit. 34, 1047 (2002)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    M. Sharif, S. Rani, Phys. Scr. 84, 055005 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    M. Sharif, S. Rani, Mod. Phys. Lett. A 26, 1657 (2011)ADSCrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    R.J. Yang, Eur. Phys. J. C 71, 1797 (2011)ADSCrossRefGoogle Scholar
  10. 10.
    R. Myrzakulov, Eur. Phys. J. C 71, 1752 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    B. Li, T.P. Sotiriou, J.D. Barrow, Phys. Rev. D 83, 104017 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    J.B. Dent, S. Dutta, E.N. Saridakis, JCAP 01, 009 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    S-H. Chen, J.B. Dent, S. Dutta, E.N. Saridakis, Phys. Rev. D 83, 023508 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    X-H. Meng, Y-B. Wang, Eur. Phys. J. C 71, 1755 (2011)ADSCrossRefGoogle Scholar
  15. 15.
    T. Wang, Phys. Rev. D 84, 024042 (2011)ADSCrossRefGoogle Scholar
  16. 16.
    L. Iorio, E.N. Saridakis, Mon. Not. R. Astron. Soc. 427, 1555 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    M. Sharif, S. Rani, Astrophys. Space Sci. 345, 217 (2013)ADSCrossRefMATHGoogle Scholar
  18. 18.
    M. Jamil, D. Momeni, R. Myrzakulov, Eur. Phys. J. C 72, 2057 (2012)CrossRefGoogle Scholar
  19. 19.
    S. Capozziello, V.F. Cardone, H. Farajollahi, A. Ravanpak, Phys. Rev. D 84, 043527 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    K. Bamba, S. Capozziello, S. Nojiri, S.D. Odintsov, Astrophys. Space Sci. 342, 155 (2012)ADSCrossRefGoogle Scholar
  21. 21.
    K. Bamba, C.Q. Geng, JCAP 11, 008 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    K. Karami, A. Abdolmaleki, JCAP 04, 007 (2012)ADSCrossRefGoogle Scholar
  23. 23.
    K. Bamba, M. Jamil, D. Momeni, R. Myrzakulov, Astrophys. Space Sci. 344, 259 (2013)ADSCrossRefMATHGoogle Scholar
  24. 24.
    J.M. Bardeen, B. Carter, S. Hawking, Commun. Math. Phys. 31, 161 (1973)ADSCrossRefMATHMathSciNetGoogle Scholar
  25. 25.
    G. Gibbons, S. Hawking, Phys. Rev. D 15, 2738 (1977)ADSCrossRefMathSciNetGoogle Scholar
  26. 26.
    T. Jacobson, Phys. Rev. Lett. 75, 1260 (1995)ADSCrossRefMATHMathSciNetGoogle Scholar
  27. 27.
    C. Eling, R. Guedens, T. Jacobson, Phys. Rev. Lett. 96, 121301 (2006)ADSCrossRefMathSciNetGoogle Scholar
  28. 28.
    K. Bamba, C-Q. Geng, S. Nojiri, S.D. Odintsov, EPL 89, 50003 (2010)ADSCrossRefGoogle Scholar
  29. 29.
    H.M. Sadjadi, Phys. Rev. D 76, 104024 (2007)ADSCrossRefMathSciNetGoogle Scholar
  30. 30.
    M. Jamil, E.N. Saridakis, M.R. Setare, JCAP 11, 032 (2010)ADSCrossRefMathSciNetGoogle Scholar
  31. 31.
    A. Sheykhi, Eur. Phys. J. C 69, 265 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    K. Karami, S. Ghaffari, Phys. Lett. B 688, 125 (2010)ADSCrossRefGoogle Scholar
  33. 33.
    K. Bamba, R. Myrzakulov, S. Nojiri, S.D. Odintsov, Phys. Rev. D 85, 104036 (2012)ADSCrossRefGoogle Scholar
  34. 34.
    U. Debnath et al., Eur. Phys. J. C 72, 1875 (2012)ADSCrossRefGoogle Scholar
  35. 35.
    H.M. Sadjadi, M. Jamil, EPL 92, 69001 (2010)ADSCrossRefGoogle Scholar
  36. 36.
    M. Sharif, A. Jawad, Int. J. Mod. Phys. D 22, 1350014 (2013)ADSCrossRefMathSciNetGoogle Scholar
  37. 37.
    K. Hayashi, T. Shirafuji, Phys. Rev. D 19, 3524 (1979)ADSCrossRefMATHMathSciNetGoogle Scholar
  38. 38.
    R. Ferraro, F. Fiorini, Phys. Lett. B 702, 75 (2011)ADSCrossRefMathSciNetGoogle Scholar
  39. 39.
    S. Nojiri, S.D. Odintsov, S. Tsujikawa, Phys. Rev. D 71, 063004 (2005)ADSCrossRefGoogle Scholar
  40. 40.
    H.M. Sadjadi, Phys. Rev. D 73, 063525 (2006)ADSCrossRefGoogle Scholar
  41. 41.
    S. Nojiri, S.D. Odintsov, Gen. Relativ. Gravit. 38, 1285 (2006)ADSCrossRefMATHMathSciNetGoogle Scholar
  42. 42.
    R.M. Wald, Phys. Rev. D 48, 3427 (1993)ADSCrossRefMathSciNetGoogle Scholar
  43. 43.
    A. Sheykhi, AM. Jamil, Gen. Relativ. Gravit. 43, 2661 (2011)ADSCrossRefMATHMathSciNetGoogle Scholar
  44. 44.
    N. Radicella, D. Pavón, J. Phys. Conf. Ser. 314, 012036 (2011)ADSCrossRefGoogle Scholar
  45. 45.
    M. Jamil, M.U. Farooq, JCAP 03, 001 (2010)ADSCrossRefGoogle Scholar
  46. 46.
    K. Karami, M. Jamil, N. Sahraei, Phys. Scr. 82, 045901 (2010)ADSCrossRefGoogle Scholar
  47. 47.
    R.X. Miao, M. Lib, Y.G. Miaoc, JCAP 11, 033 (2011)ADSCrossRefGoogle Scholar
  48. 48.
    D. Bak, S.J. Rey, Class. Quantum Grav. 17, L83 (2000)ADSCrossRefMATHMathSciNetGoogle Scholar
  49. 49.
    M. Li, Phys. Lett. B 603, 1 (2004)ADSCrossRefGoogle Scholar
  50. 50.
    S. Hod, Class. Quantum Grav. 21, L97 (2004)ADSCrossRefMATHMathSciNetGoogle Scholar
  51. 51.
    M. Sharif, S. Rani, Astrophys. Space Sci. 346, 573 (2013)ADSCrossRefMATHGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the PunjabLahorePakistan

Personalised recommendations