International Journal of Theoretical Physics

, Volume 51, Issue 10, pp 3168–3185 | Cite as

Study of Thermodynamic Quantities in Generalized Gravity Theories

  • Surajit Chattopadhyay
  • Ujjal Debnath
  • Samarpita Bhattacharya
Article

Abstract

In this work, we have studied the thermodynamic quantities like temperature of the universe, heat capacity and squared speed of sound in generalized gravity theories like Brans-Dicke, Hořava-Lifshitz and f(R) gravities. We have considered the universe filled with dark matter and dark energy. Also we have considered the equation of state parameters for open, closed and flat models. We have observed that in all cases the equation of state behaves like quintessence. The temperature and heat capacity of the universe are found to decrease with the expansion of the universe in all cases. In Brans-Dicke and f(R) gravity theories the squared speed of sound is found to exhibit increasing behavior for open, closed and flat models and in Hořava-Lifshitz gravity theory it is found to exhibit decreasing behavior for open and closed models with the evolution of the universe. However, for flat universe, the squared speed of sound remains constant in Hořava-Lifshitz gravity.

Keywords

Thermodynamic quantities Generalized gravity theories Equation of state parameter Squared speed of sound 

Notes

Acknowledgements

The authors are thankful to the anonymous reviewers for their constructive suggestions. The first two authors are thankful to the Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, India for providing Visiting Associateship, under which this work was carried out. The third author wishes to sincerely acknowledge the warm hospitality provided by IUCAA, Pune, where part of the work was carried out during a scientific visit.

References

  1. 1.
    Carloni, S., Chaichian, M., Nojiri, S., Odintsov, S.D., Oksanen, M., Tureanu, A.: Phys. Rev. D 82, 065020 (2010) ADSCrossRefGoogle Scholar
  2. 2.
    Nojiri, S., Odintsov, S.D.: In: Proceedings of the 42nd Karpacz Winter School of Theoretical Physics: Current Mathematical Topics in Gravitation and Cosmology, Ladek, Poland (2006). eConf C0602061 Google Scholar
  3. 3.
    Capozziello, S., Nojiri, S., Odintsov, S.D.: Phys. Lett. B 634, 93 (2006) ADSCrossRefGoogle Scholar
  4. 4.
    Dolgova, A.D., Kawasaki, M.: Phys. Lett. B 573, 1 (2003) ADSCrossRefGoogle Scholar
  5. 5.
    Nojiri, S., Odintsov, S.D.: Phys. Rev. D 68, 123512 (2003) MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    Carroll, S.M., De Felice, A., Duvvuri, V., Easson, D.A., Trodden, M., Turner, M.S.: Phys. Rev. D 71, 063513 (2005) ADSCrossRefGoogle Scholar
  7. 7.
    Nojiri, S., Odintsov, S.D.: Gen. Relativ. Gravit. 36, 1765 (2004) MathSciNetADSMATHCrossRefGoogle Scholar
  8. 8.
    Nojiri, S., Odintsov, S.D.: Phys. Lett. B 576, 5 (2003) MathSciNetADSMATHCrossRefGoogle Scholar
  9. 9.
    Nojiri, S., Odintsov, S.D.: Int. J. Geom. Methods Mod. Phys. 4, 115 (2007) MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Nojiri, S., Odintsov, S.D.: J. Phys. Conf. Ser. 66, 012005 (2007) ADSCrossRefGoogle Scholar
  11. 11.
    Hořava, P.: Phys. Rev. D 79, 084008 (2009) MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Faulkner, T., Tegmark, M., Bunn, E.F., Mao, Y.: Phys. Rev. D 76, 063505 (2007) MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    Colgain, E.O., Yavartanoo, H.: J. High Energy Phys. 08, 021 (2009) ADSCrossRefGoogle Scholar
  14. 14.
    Kluson, J.: J. High Energy Phys. 07, 038 (2010) MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    Jamil, M., Saridakis, E.N., Setare, M.R.: J. Cosmol. Astropart. Phys. 11, 032 (2010) MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    Brans, C., Dicke, R.H.: Phys. Rev. 124, 925 (1961) MathSciNetADSMATHCrossRefGoogle Scholar
  17. 17.
    Chen, X., Kamionkowski, M.: Phys. Rev. D 60, 104036 (1999) ADSCrossRefGoogle Scholar
  18. 18.
    Sheykhi, A.: Phys. Lett. B 681, 205 (2009) MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    Sheykhi, A.: Phys. Rev. D 81, 023525 (2010) ADSCrossRefGoogle Scholar
  20. 20.
    Setare, M.R.: Phys. Lett. B 644, 99 (2007) MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    Banerjee, N., Pavon, D.: Phys. Lett. B 647, 477 (2007) MathSciNetADSCrossRefGoogle Scholar
  22. 22.
    Xu, L., Li, W., Lu, J.: Eur. Phys. J. C 60, 135 (2009) MathSciNetADSMATHCrossRefGoogle Scholar
  23. 23.
    Gong, Y.: Phys. Rev. D 61, 043505 (2000) MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    Nayak, B., Singh, L.P.: Mod. Phys. Lett. A 24, 1785 (2009) MathSciNetADSMATHCrossRefGoogle Scholar
  25. 25.
    Setare, M.R., Jamil, M.: Phys. Lett. B 690, 1 (2010) ADSCrossRefGoogle Scholar
  26. 26.
    Das, S., Banerjee, N.: Phys. Rev. D 78, 043512 (2008) ADSCrossRefGoogle Scholar
  27. 27.
    Jacobson, T.: Phys. Rev. Lett. 75, 1260 (1995) MathSciNetADSMATHCrossRefGoogle Scholar
  28. 28.
    Padmanabhan, T.: Class. Quantum Gravity 19, 5387 (2002) MathSciNetADSMATHCrossRefGoogle Scholar
  29. 29.
    Padmanabhan, T.: Phys. Rep. 406, 49 (2005) MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    Jamil, M., Hussain, I., Farooq, M.U.: Astrophys. Space Sci. 335, 339 (2011) ADSMATHCrossRefGoogle Scholar
  31. 31.
    Debnath, U., Jamil, M.: Astrophys. Space Sci. 335, 545 (2011) ADSCrossRefGoogle Scholar
  32. 32.
    Jamil, M., Akbar, M.: Gen. Relativ. Gravit. 43, 1061 (2011) MathSciNetADSMATHCrossRefGoogle Scholar
  33. 33.
    Jamil, M., Saridakis, E.N., Setare, M.R.: Phys. Rev. D 81, 023007 (2010) ADSCrossRefGoogle Scholar
  34. 34.
    Setare, M.R., Shafei, S.: J. Cosmol. Astropart. Phys. 09, 011 (2006) ADSCrossRefGoogle Scholar
  35. 35.
    Davies, P.C.W.: Class. Quantum Gravity 4, L225 (1987) ADSCrossRefGoogle Scholar
  36. 36.
    Sadjadi, H.M.: Phys. Rev. D 73, 063525 (2006) ADSCrossRefGoogle Scholar
  37. 37.
    Izquierdo, G., Pavon, D.: Phys. Lett. B 639, 1 (2006) MathSciNetADSCrossRefGoogle Scholar
  38. 38.
    Mohseni Sadjadi, H.: Phys. Lett. B 645, 108 (2007) MathSciNetADSCrossRefGoogle Scholar
  39. 39.
    Wang, B., Gong, Y., Abdalla, E.: Phys. Rev. D 74, 083520 (2006) ADSCrossRefGoogle Scholar
  40. 40.
    Hu, W., Sawicki, I.: Phys. Rev. D 76, 064004 (2007) ADSCrossRefGoogle Scholar
  41. 41.
    Nojiri, S., Odintsov, S.D.: Phys. Lett. B 576, 5 (2003) MathSciNetADSMATHCrossRefGoogle Scholar
  42. 42.
    Amendola, L., Gannouji, R., Polarski, D., Tsujikawa, S.: Phys. Rev. D 75, 083504 (2007) ADSCrossRefGoogle Scholar
  43. 43.
    Sadjadi, H.M.: Phys. Rev. D 76, 104024 (2007) MathSciNetADSCrossRefGoogle Scholar
  44. 44.
    Bamba, K., Geng, C.-Q.: Phys. Lett. B 679, 282 (2009) MathSciNetADSCrossRefGoogle Scholar
  45. 45.
    Wu, S.-F., Wang, B., Yang, G.-H.: Nucl. Phys. B 799, 330 (2008) MathSciNetADSMATHCrossRefGoogle Scholar
  46. 46.
    Mazumder, N., Chakraborty, S.: Int. J. Theor. Phys. 50, 251 (2011) MathSciNetMATHCrossRefGoogle Scholar
  47. 47.
    Wu, S.-F., Wang, B., Yang, G.-H., Zhang, P.-M.: Class. Quantum Gravity 25, 235018 (2008) MathSciNetADSCrossRefGoogle Scholar
  48. 48.
    Cai, R.-G., Cao, L.-M.: Nucl. Phys. B 785, 135 (2007) MathSciNetADSMATHCrossRefGoogle Scholar
  49. 49.
    Sheykhi, A., Wang, B., Cai, R.-G.: Nucl. Phys. B 779, 1 (2007) MathSciNetADSMATHCrossRefGoogle Scholar
  50. 50.
    Sheykhi, A.: J. Cosmol. Astropart. Phys. 05, 019 (2009) ADSCrossRefGoogle Scholar
  51. 51.
    Wang, A., Wu, Y.: J. Cosmol. Astropart. Phys. 07, 012 (2009) ADSCrossRefGoogle Scholar
  52. 52.
    Nishioka, T.: Class. Quantum Gravity 26, 242001 (2009) MathSciNetADSCrossRefGoogle Scholar
  53. 53.
    Cai, R.-G., Ohta, N.: Phys. Rev. D 81, 084061 (2010) ADSCrossRefGoogle Scholar
  54. 54.
    Kim, H., Kim, Y.: Nuovo Cimento B 112, 329 (1997) ADSGoogle Scholar
  55. 55.
    Dehghani, M.H., Pakravan, J., Hendi, S.H.: Phys. Rev. D 74, 104014 (2006) MathSciNetADSCrossRefGoogle Scholar
  56. 56.
    Gong, Y., Wang, A.: Phys. Rev. Lett. 99, 211301 (2007) MathSciNetADSCrossRefGoogle Scholar
  57. 57.
    Bhattacharya, S., Debnath, U.: Can. J. Phys. 89, 883 (2010) ADSCrossRefGoogle Scholar
  58. 58.
    Bamba, K., Geng, C.-Q.: Phys. Lett. B 679, 282 (2009) MathSciNetADSCrossRefGoogle Scholar
  59. 59.
    Akbar, M., Cai, R.-G.: Phys. Lett. B 648, 243 (2007) MathSciNetADSCrossRefGoogle Scholar
  60. 60.
    Sadjadi, H.M.: Phys. Rev. D 76, 104024 (2007) MathSciNetADSCrossRefGoogle Scholar
  61. 61.
    Bhattacharya, S., Debnath, U.: Int. J. Mod. Phys. D 20, 1191 (2011) MathSciNetADSCrossRefGoogle Scholar
  62. 62.
    Copeland, E.J., Sami, M., Tsujikawa, S.: Int. J. Mod. Phys. D 15, 1753 (2006) MathSciNetADSMATHCrossRefGoogle Scholar
  63. 63.
    Sahnia, V., Starobinsky, A.: Int. J. Mod. Phys. D 15, 2105 (2006) ADSCrossRefGoogle Scholar
  64. 64.
    Gong, Y., Wang, B., Wang, A.: Phys. Rev. D 75, 123516 (2007) MathSciNetADSCrossRefGoogle Scholar
  65. 65.
    Akbar, M.: Chin. Phys. Lett. 25, 4199 (2008) ADSCrossRefGoogle Scholar
  66. 66.
    Brevik, I., Nojiri, S., Odintsov, S.D., Vanzo, L.: Phys. Rev. D 70, 043520 (2004) MathSciNetADSCrossRefGoogle Scholar
  67. 67.
    Santos, C., Gregory, R.: Ann. Phys. 258, 111 (1997) MathSciNetADSMATHCrossRefGoogle Scholar
  68. 68.
    Kiritsis, E., Kofinas, G.: Nucl. Phys. B 821, 467 (2009) MathSciNetADSMATHCrossRefGoogle Scholar
  69. 69.
    Jamil, M., Saridakis, E.N., Setare, M.R.: J. Cosmol. Astropart. Phys. 11, 032 (2010) MathSciNetADSCrossRefGoogle Scholar
  70. 70.
    Nojiri, S., Odintsov, S.D.: Phys. Lett. B 657, 238 (2007) MathSciNetADSCrossRefGoogle Scholar
  71. 71.
    Bamba, K., Geng, C.-Q.: Phys. Lett. B 679, 282 (2009) MathSciNetADSCrossRefGoogle Scholar
  72. 72.
    Steinhardt, P.J.: Philos. Trans. R. Soc. Lond. A 361, 2497 (2003) ADSMATHCrossRefGoogle Scholar
  73. 73.
    Mazur, P.O., Mottola, E.: Proc. Natl. Acad. Sci. USA 101, 9545 (2004) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Surajit Chattopadhyay
    • 1
  • Ujjal Debnath
    • 2
  • Samarpita Bhattacharya
    • 2
  1. 1.Department of Computer Application (Mathematics Section)Pailan College of Management and TechnologyBengal Pailan ParkIndia
  2. 2.Department of MathematicsBengal Engineering and Science UniversityShibpurIndia

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