Skip to main content
Log in

A modified gravity theory with time-dependent exponent

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

Abstract

In this work, we discussed the cosmological consequences of a modified gravity theory characterized by f(R) = R n(t) where n(t) = 1 + B(tt 0)ε, B and ε are free parameters in the theory and a Hubble parameter which varies as \(H(t) = A\sqrt R\) where A is a real positive parameter. For some explicit and reasonable values of the free parameters of the theory, our proposal contains several novel features which were discussed in some details.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. B.R. Schmidt et al., Astrophys. J. 507, 46 (1998).

    Article  ADS  Google Scholar 

  4. P.J. Steinhardt, L. Wang, I. Zlatev, Phys. Rev. D 59, 123504 (1999).

    Article  ADS  Google Scholar 

  5. M. Persic, P. Salucci, F. Stel, Mon. Not. R. Astron. Soc. 281, 27 (1996).

    ADS  Google Scholar 

  6. A.G. Riess et al., Astrophys. J. 607, 665 (2004).

    Article  ADS  Google Scholar 

  7. J.S. Alcaniz, Phys. Rev. D 69, 083521 (2004).

    Article  ADS  Google Scholar 

  8. H. Zhan, L. Knox, Astrophys. J. 644, 663 (2006).

    Article  ADS  Google Scholar 

  9. A.H. Jaffe et al., Phys. Rev. Lett. 86, 3475 (2001).

    Article  ADS  Google Scholar 

  10. WMAP Collaboration (D.N. Spergel et al.), Astrophys. J. Suppl. 148, 175 (2003).

    Article  ADS  Google Scholar 

  11. J. Peacock et al., Nature 410, 169 (2001).

    Article  ADS  Google Scholar 

  12. SDSS Collaboration (M. Tegmark et al.), Phys. Rev. D 69, 103501 (2004).

    Article  ADS  Google Scholar 

  13. C.B. Netterfield et al., Astrophys. J. 571, 604 (2002).

    Article  ADS  Google Scholar 

  14. A.T. Lee et al., Astrophys. J. 561, L1 (2001).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. A.H. Guth, Phys. Rev. D 23, 347 (1981).

    Article  ADS  Google Scholar 

  17. A.D. Linde, Phys. Lett. B 108, 389 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  18. J. Oukbir, A. Blanchard, Astron. Astrophys. 317, 10 (1997).

    ADS  Google Scholar 

  19. Z.-H. Zhu, M.-K. Fujimoto, X.-T. He, Astrophys. J. 603, 365 (2004).

    Article  ADS  Google Scholar 

  20. M. Douspis, C. R. Phys. 4, 881 (2003).

    Article  ADS  Google Scholar 

  21. Y. Wang, K. Freese, Phys. Lett. B 632, 449 (2006).

    Article  ADS  Google Scholar 

  22. A. Sheykhi, M. Sadegh Movahed, arXiv:1104.4713.

  23. M. Malekjani, A. Khodam-Mohammadi, M. Taji, Int. J. Theor. Phys. 50, 3112 (2011).

    Article  MATH  Google Scholar 

  24. M. Malekjani, A. Khodam-Mohammadi, N. Nazari-Pooya, Astrophys. Space Sci. 332, 515 (2011).

    Article  ADS  Google Scholar 

  25. K. Karami, A. Abdolmaleki, Astrophys. Space Sci. 330, 133 (2010).

    Article  ADS  MATH  Google Scholar 

  26. V. Sahni, A. Starobinsky, Int. J. Mod. Phys. D 9, 373 (2000).

    ADS  Google Scholar 

  27. B. Ratra, P.J.E. Peebles, Phys. Rev. D 37, 3406 (1988).

    Article  ADS  Google Scholar 

  28. C. Wetterich, Nucl. Phys. B 302, 668 (1988).

    Article  ADS  Google Scholar 

  29. A.R. Liddle, R.J. Scherrer, Phys. Rev. D 59, 023509 (1999).

    Article  ADS  Google Scholar 

  30. Z.K. Guo, N. Ohta, Y.Z. Zhang, Mod. Phys. Lett. A 22, 883 (2007).

    Article  ADS  MATH  Google Scholar 

  31. S. Dutta, E.N. Saridakis, R.J. Scherrer, Phys. Rev. D 79, 103005 (2009).

    Article  ADS  Google Scholar 

  32. T. Chiba, T. Okabe, M. Yamaguchi, Phys. Rev. D 62, 023511 (2000).

    Article  ADS  Google Scholar 

  33. T. Chiba, Phys. Rev. D 66, 063514 (2002).

    Article  ADS  Google Scholar 

  34. C. Armendariz-Picon, V. Mukhanov, P.J. Steinhardt, Phys. Rev. Lett. 85, 4438 (2000).

    Article  ADS  Google Scholar 

  35. C. Armendariz-Picon, V. Mukhanov, P.J. Steinhardt, Phys. Rev. D 63, 103510 (2001).

    Article  ADS  Google Scholar 

  36. A. Starobinsky, Gravit. Cosmol. 6, 157 (2000).

    ADS  MATH  Google Scholar 

  37. R. Caldwell, M. Kamionkowski, N. Weinberg, Phys. Rev. Lett. 91, 071301 (2003).

    Article  ADS  Google Scholar 

  38. D. Huterer, A. Cooray, Phys. Rev. D 71, 023506 (2005).

    Article  ADS  Google Scholar 

  39. B. Feng, X.L. Wang, X.M. Zhang, Phys. Lett. B 607, 35 (2005).

    Article  ADS  Google Scholar 

  40. P.F. Gonzalez-Diaz, J.A. Jimenez-Madrid, Phys. Lett. B 596, 16 (2004).

    Article  ADS  Google Scholar 

  41. S. Capozziello, S. Nojiri, S.D. Odintsov, Phys. Lett. B 632, 597 (2006).

    Article  ADS  Google Scholar 

  42. J.D. Barrow, Class. Quantum Grav. 21, 79 (2004).

    Article  MathSciNet  ADS  Google Scholar 

  43. H. Stefancic, Phys. Rev. D 71, 084024 (2005).

    Article  ADS  Google Scholar 

  44. S. Nojiri, S.D. Odintsov, S. Tsujikawa, Phys. Rev. D 71, 063004 (2005).

    Article  ADS  Google Scholar 

  45. R.A. El-Nabulsi, Braz. J. Phys. 40, 150 (2010).

    Google Scholar 

  46. M.R. Setare, M. Saridakis, JCAP 09, 026 (2008).

    ADS  Google Scholar 

  47. M.R. Setare, M. Saridakis, Phys. Lett. B 668, 177 (2008).

    Article  ADS  Google Scholar 

  48. M.R. Setare, S. Shafei, JCAP 09, 011 (2006).

    ADS  Google Scholar 

  49. M.R. Setare, Phys. Lett. B 648, 329 (2007).

    Article  ADS  Google Scholar 

  50. M.R. Setare, JCAP 01, 023 (2007).

    MathSciNet  ADS  Google Scholar 

  51. R. Tavakol, G. Ellis, Phys. Lett. B 469, 33 (1999).

    MathSciNet  Google Scholar 

  52. R. Esther, D. Lowe, Phys. Rev. Lett. 82, 4967 (1999).

    Article  MathSciNet  ADS  Google Scholar 

  53. A. Cohen, D. Kaplan, A. Nelson, Phys. Rev. Lett. 82, 4971 (1999).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  54. S. Thomas, Phys. Rev. Lett. 89, 081301 (2002).

    Article  MathSciNet  ADS  Google Scholar 

  55. S.D. Hsu, Phys. Lett. B 594, 1 (2004).

    Article  ADS  Google Scholar 

  56. M. Li, Phys. Lett. B 603, 1 (2004).

    Article  ADS  Google Scholar 

  57. A.W. Brookfield, C. van de Bruck, D.F. Mota, D. Tocchini-Valentini, Phys. Rev. D 73, 083515 (2006) (E) 76.

    Article  ADS  Google Scholar 

  58. G.Y. Chitov, T. August, A. Natarajan, T. Kahniashvili, Phys. Rev. D 83, 045033 (2011).

    Article  ADS  Google Scholar 

  59. G.-Bo Zhao, J.-Qing Xia, B. Feng, X. Zhang, Int. J. Mod. Phys. D 16, 1229 (2007).

    Article  ADS  MATH  Google Scholar 

  60. J.-Qing Xia, G.-Bo Zhao, B. Feng, X. Zhang, JCAP 09, 015 (2006).

    Google Scholar 

  61. B. Feng, M. Li, Y.-Song Piao, X. Zhang, Phys. Lett. B 634, 101 (2006).

    Article  ADS  Google Scholar 

  62. M.R. Setare, Phys. Lett. B 641, 130 (2006).

    Article  MathSciNet  ADS  Google Scholar 

  63. J. Sadeghi, M.R. Setare, A. Banijamali, F. Milani, Phys. Lett. B 662, 92 (2008).

    Article  ADS  Google Scholar 

  64. M.R. Setare, J. Sadeghi, A.R. Amani, Phys. Lett. B 660, 299 (2008).

    Article  ADS  Google Scholar 

  65. M. Umar Farooq, M. Jamil, U. Debnath, Astrophys. Space Sci. 334, 243 (2011).

    Article  ADS  Google Scholar 

  66. M. Jamil, A. Sheykhi, Int. J. Theor. Phys. 50, 625 (2011).

    Article  MATH  MathSciNet  Google Scholar 

  67. V. Faraoni, Phys. Rev. D 83, 124004 (2011).

    Article  ADS  Google Scholar 

  68. C. Brans, R.H. Dicke, Phys. Rev. 124, 925 (1962).

    Article  MathSciNet  ADS  Google Scholar 

  69. P. Jordan, Schwerkraft und Weltall, Grundlagen der Theoretische Kosmologie (Vieweg und Sohn, Braunschweig, 1955).

  70. C. de Rham, Phys. Lett. B 688, 137 (2010).

    Article  MathSciNet  ADS  Google Scholar 

  71. H. Won Lee, K. Yee Kim, Y. Soo Myung, arXiv:1106.6114.

  72. K. Hinterbichler, arXiv:1105.3735.

  73. K. Lee, F.A. Jenet, R.H. Price, N. Wex, M. Kramer, Astrophys. J. 722, 1589 (2010).

    Article  ADS  Google Scholar 

  74. A.I. Vainshtein, Phys. Lett. B 39, 393 (1972).

    Article  ADS  Google Scholar 

  75. C. Deffayet, G.R. Dvali, G. Gabadadze, A.I. Vainshtein, Phys. Rev. D 65, 044026 (2002).

    Article  ADS  Google Scholar 

  76. N. Arkani-Hamed, H. Georgi, M.D. Schwartz, Ann. Phys. (N.Y.) 305, 96 (2003).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  77. A. Gruzinov, New Astron. 10, 311 (2005).

    Article  ADS  Google Scholar 

  78. A. Jenkens, Int. J. Mod. Phys. D 18, 2249 (2009).

    Article  ADS  Google Scholar 

  79. R. Durrer, arXiv:hep-th/0507006.

  80. A. Arbey, F. Mahmoudi, Phys. Rev. D 75, 063513 (2007).

    Article  MathSciNet  ADS  Google Scholar 

  81. L. Parker, J.Z. Simon, Phys. Rev. D 47, 1339 (1993).

    Article  MathSciNet  ADS  Google Scholar 

  82. S. Nesseris, A. De Felice, S. Tsujikawa, Phys. Rev. D 82, 124054 (2010).

    Article  ADS  Google Scholar 

  83. D.F. Mota, M. Sandstad, T. Zlosnik, JHEP 012, 051 (2010).

    Article  ADS  Google Scholar 

  84. C. Burrage, C. de Rham, D. Seery, A.J. Tolley, JCAP 01, 014 (2011).

    ADS  Google Scholar 

  85. U. Debnath, S. Chattopadhyay, M. Jamil, arXiv:1107.0541.

  86. M. Jamil, D. Momeni, M.A. Rashid, arXiv:1106.2974.

  87. R.A. El-Nabulsi, Commun. Theor. Phys. 54, 16 (2010).

    Article  ADS  MATH  Google Scholar 

  88. R.A. El-Nabulsi, Rom. Rep. Phys. 59, 763 (2007).

    Google Scholar 

  89. R.A. El-Nabulsi, Fiz. B 19, 103 (2010).

    Google Scholar 

  90. V. Faraoni, Phys. Rev. D 83, 124044 (2011).

    Article  ADS  Google Scholar 

  91. L. Amendola, R. Gannouji, D. Polarski, S. Tsujikawa, Phys. Rev. D 75, 083504 (2007).

    Article  ADS  Google Scholar 

  92. S. Capozziello, S. Tsujikawa, Phys. Rev. D 77, 107501 (2008).

    Article  ADS  Google Scholar 

  93. A.D. Dolgov, M. Kawasaki, Phys. Lett. B 573, 1 (2003).

    Article  ADS  MATH  Google Scholar 

  94. S. Capozziello, M. De Laurentis, V. Faraoni, Open Astron. J. 3, 49 (2010).

    Article  ADS  Google Scholar 

  95. M. Kaplinghat, G. Steigman, I. Tkachev, T.P. Walker, Phys. Rev. D 59, 043514 (1999).

    Article  ADS  Google Scholar 

  96. M. Sethi, A. Batra, D. Lohiya, Phys. Rev. D 60, 108301 (1999).

    Article  ADS  Google Scholar 

  97. M. Kaplinghat, G. Steigman, T.P. Walker, Phys. Rev. D 61, 103507 (2000).

    Article  ADS  Google Scholar 

  98. D. Lohiya, M. Sethi, Class. Quantum Grav. 16, 1545 (1999).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  99. G. Sethi, A. Dev, D. Jain, Phys. Lett. B 624, 135 (2005).

    Article  ADS  Google Scholar 

  100. A. Dev, D. Jain, D. Lohiya, arXiv:0804.3491.

  101. A. Dev, M. Sethi, D. Lohiya, Phys. Lett. B 504, 207 (2011).

    ADS  Google Scholar 

  102. D. Jain, A. Dev, J.S. Alcaniz, Class. Quantum Grav. 30, 4163 (2003).

    MathSciNet  Google Scholar 

  103. C. Kaeonikhom, B. Gumjudpai, E.N. Saridakis, Phys. Lett. B 695, 45 (2011).

    Article  ADS  Google Scholar 

  104. A.D. Doglov, Phys. Rev. D 55, 5881 (1997).

    Article  ADS  Google Scholar 

  105. J. Kujat et al., Astrophys. J. 572, 1 (2002).

    Article  ADS  Google Scholar 

  106. M. Bartelmann et al., New Astron. Rev. 49, 199 (2005).

    Article  ADS  Google Scholar 

  107. I. Brevik, O.G. Gorbunova, A.V. Timoshkin, Eur. Phys. J. C 51, 179 (2007).

    Article  ADS  Google Scholar 

  108. A.A. Usmani et al., Mon. Not. R. Astron. Soc. Lett. 386, L92 (2008).

    Article  ADS  Google Scholar 

  109. R.A. El-Nabulsi, Res. Astron. Astrophys. 11, 759 (2011).

    Article  ADS  Google Scholar 

  110. R.A. El-Nabulsi, Res. Astron. Astrophys. 11, 888 (2011).

    Article  ADS  Google Scholar 

  111. R.A. Knop et al., Astrophys. J. 598, 102 (2003).

    Article  ADS  Google Scholar 

  112. C. Cattoen, M. Visser, Phys. Rev. D 78, 063501 (2008).

    Article  ADS  Google Scholar 

  113. G. Oliveira-Neto, G.A. Monerat, E.V. Corrêa Silva, C. Neves, L.G. Ferreira, arXiv:1106.3963.

  114. S. Kalyana Rama, Phys. Rev. D 79, 124031 (2009).

    Article  ADS  Google Scholar 

  115. R.A. El-Nabulsi, Int. J. Mod. Phys. D 18, 289 (2009).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  116. R.A. El-Nabulsi, Int. J. Mod. Phys. D 18, 691 (2009).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  117. R.A. El-Nabulsi, Commun. Theor. Phys. 53, 869 (2010).

    Article  ADS  MATH  Google Scholar 

  118. R.A. El-Nabulsi, Gen. Relativ. Gravit. 42, 1361 (2010).

    ADS  Google Scholar 

  119. R.A. El-Nabulsi, Gen. Relativ. Gravit. 42, 1875 (2010).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  120. R.A. El-Nabulsi, Astrophys. Space Sci. 327, 173 (2010).

    Article  ADS  Google Scholar 

  121. R.A. El-Nabulsi, Astrophys. Space Sci. 325, 149 (2010).

    Article  ADS  MATH  Google Scholar 

  122. T. Harko, T.S. Koivisto, F.S.N. Lobo, Mod. Phys. Lett. A 26, 1467 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  123. N.J. Poplawski, Phys. Rev. D 74, 084032 (2006).

    Article  ADS  Google Scholar 

  124. M. Jamil, I. Hussain, U.M. Farooq, Astrophys. Space Sci. 335, 339 (2001).

    Article  ADS  Google Scholar 

  125. A.D. Doglov, M. Kawasaki, Phys. Lett. B 573, 1 (2003).

    Article  ADS  Google Scholar 

  126. M.S. Berman, Nuovo Cimento B 74, 182 (1983).

    Article  ADS  Google Scholar 

  127. M.S. Berman, R.M. Gomide, Gen. Relativ. Gravit. 20, 191 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  128. S. Ram, M. Zeyauddin, C.P. Singh, Pramana J. Phys. 72, 415 (2009).

    Article  ADS  Google Scholar 

  129. S. Weinberg, Gravitation and Cosmology (Wiley, NY, 1972).

  130. C.P. Singh, S. Kumar, Int. J. Mod. Phys. D 15, 419 (2006).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  131. C.P. Singh, S. Kumar, Pramana J. Phys. 68, 707 (2007).

    Article  ADS  Google Scholar 

  132. S. Kumar, C.P. Singh, Astrophys. Space Sci. 312, 57 (2007).

    Article  ADS  MATH  Google Scholar 

  133. S. Kumar, C.P. Singh, Int. J. Theor. Phys. 47, 1722 (2008).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. A. El-Nabulsi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

El-Nabulsi, R.A. A modified gravity theory with time-dependent exponent. Eur. Phys. J. Plus 126, 114 (2011). https://doi.org/10.1140/epjp/i2011-11114-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2011-11114-9

Keywords

Navigation