Astrophysics and Space Science

, Volume 355, Issue 2, pp 405–411 | Cite as

Reconstructing f(R), f(G), f(T), and Einstein-Aether gravities from entropy-corrected (m,n) type pilgrim dark energy

Original Article

Abstract

First, we describe the ordinary holographic dark energy (HDE), (m,n) type holographic dark energy, entropy-corrected holographic dark energy (ECHDE) for logarithmic and power-law versions and pilgrim dark energy (PDE) models. Next, we introduce the (m,n) type pilgrim dark energy and its entropy-corrected versions of logarithmic and power-law forms i.e., (m,n) type LECPDE and PLECPDE models. The main motivation of the work is to have reconstructions of f(R), f(G), f(T), and Einstein-Aether gravities from (m,n) type entropy-corrected pilgrim dark energy (ECPDE). Briefly the idea of our proposed entropy-corrected (m,n) type pilgrim dark energy model is discussed. We also discuss the modified Friedmann equations for f(R), f(G), f(T), and Einstein-Aether gravities and then from the equations we find the effective density and pressure for the f(R), f(G), f(T), and Einstein-Aether gravities sectors, respectively. These can be treated as an effective dark energy. Assuming the power-law solution of the scale factor, at δ , we can reconstruct the unknown functions of f(R), f(G), f(T), and F(K) of Einstein-Aether gravities from logarithmic and power-law corrected versions of ECPDE. Finally, we give some cosmological implications of the reconstructed models.

Keywords

Modified gravity Dark energy Correspondence 

Notes

Acknowledgements

The author is thankful for warm hospitality to IUCAA, Pune, India, where part of the work was carried out. The author is thankful to CSIR, Govt. of India for providing research project grant (No. 03(1206)/12/EMR-II).

References

  1. Abdalla, M.C.B., Nojiri, S., Odintsov, S.D.: Class. Quantum Gravity 22, L35 (2005)ADSCrossRefGoogle Scholar
  2. Antoniadis, I., et al.: Nucl. Phys. B 415, 497 (1994)ADSCrossRefGoogle Scholar
  3. Armendariz-Picon, C., Mukhanov, V.F., Steinhardt, P.J.: Phys. Rev. Lett. 85, 4438 (2000)ADSCrossRefGoogle Scholar
  4. Banerjee, R., Modak, S.K.: J. High Energy Phys. 0905, 063 (2009)ADSCrossRefGoogle Scholar
  5. Barrow, J.D.: Phys. Rev. D 85, 047503 (2012)ADSCrossRefGoogle Scholar
  6. Bengochca, G., Ferraro, R.: Phys. Rev. D 79, 124019 (2009)ADSCrossRefGoogle Scholar
  7. Brans, C., Dicke, H.: Phys. Rev. 124, 925 (1961)ADSMathSciNetCrossRefGoogle Scholar
  8. Cai, Y.-F.: et al. arXiv:1104.4349v2 (2011)
  9. Caldwell, R.R.: Phys. Lett. B 545, 23 (2002)ADSCrossRefGoogle Scholar
  10. Caldwell, R.R., et al.: Phys. Rev. Lett. 80, 1582 (1998)ADSCrossRefGoogle Scholar
  11. Chatterjee, A., Majumder, P.: Phys. Rev. Lett. 92, 141301 (2004)ADSMathSciNetCrossRefGoogle Scholar
  12. Chattopadhyay, S., Debnath, U.: Int. J. Theor. Phys. 50, 315 (2011)CrossRefGoogle Scholar
  13. Cohen, A.G., Kaplan, D.B., Nelson, A.E.: Phys. Rev. Lett. 82, 4971 (1999)ADSMathSciNetCrossRefGoogle Scholar
  14. Copeland, E.J., Sami, M., Tsujikawa, S.: Int. J. Mod. Phys. D 15, 1753 (2006)ADSCrossRefGoogle Scholar
  15. Das, S., Shankaranarayanan, S., Sur, S.: Phys. Rev. D 77, 064013 (2008)ADSCrossRefGoogle Scholar
  16. Debnath, U., Jamil, M.: Astrophys. Space Sci. 335, 545 (2011)ADSCrossRefGoogle Scholar
  17. Dutta, J., Debnath, U.: Int. J. Theor. Phys. 51, 639 (2012)CrossRefGoogle Scholar
  18. Dvali, G.R., Gabadadze, G., Porrati, M.: Phys. Lett. B 484, 112 (2000)ADSCrossRefGoogle Scholar
  19. Enqvist, K., Hannested, S., Sloth, M.S.: J. Cosmol. Astropart. Phys. 2, 004 (2005)ADSCrossRefGoogle Scholar
  20. Farooq, M.U., Jamil, M., Rashid, M.A.: Int. J. Theor. Phys. 49, 2278 (2010)CrossRefGoogle Scholar
  21. Farooq, M.U., Jamil, M., Momeni, D., Myrzakulov, R.: Can. J. Phys. 91, 703 (2013)ADSCrossRefGoogle Scholar
  22. Felice, A.D., Tsujikawa, T.: arXiv:1002.4928 [gr-qc] (2010)
  23. Fischler, W., Susskind, L.: hep-th/9806039 (1998)
  24. Gasperini, M.: Class. Quantum Gravity 4, 485 (1987)ADSMathSciNetCrossRefGoogle Scholar
  25. Gasperini, M., et al.: Phys. Rev. D 65, 023508 (2002)ADSCrossRefGoogle Scholar
  26. Ghosh, A., Mitra, P.: Phys. Rev. D 71, 027502 (2004)ADSCrossRefGoogle Scholar
  27. Gong, Y.: Phys. Rev. D 70, 064029 (2004)ADSCrossRefGoogle Scholar
  28. Gumjudpai, B., Ward, J.: Phys. Rev. D 80, 023528 (2009)ADSCrossRefGoogle Scholar
  29. Horava, P.: J. High Energy Phys. 0903, 020 (2009)ADSMathSciNetCrossRefGoogle Scholar
  30. Hsu, S.D.H.: Phys. Lett. B 594, 13 (2004)ADSCrossRefGoogle Scholar
  31. Jacobson, T., Mattingly, D.: Phys. Rev. D 64, 024028 (2001)ADSMathSciNetCrossRefGoogle Scholar
  32. Jamil, M., Farooq, M.U.: J. Cosmol. Astropart. Phys. 03, 001 (2010)ADSCrossRefGoogle Scholar
  33. Jamil, M., Farooq, M.U.: J. Cosmol. Astropart. Phys. 03, 001 (2010)ADSCrossRefGoogle Scholar
  34. Jamil, M., Sheykhi, A.: Int. J. Theor. Phys. 50, 625 (2011)CrossRefGoogle Scholar
  35. Kamenshchik, A.Y., Moschella, U., Pasquier, V.: Phys. Lett. B 511, 265 (2001)ADSCrossRefGoogle Scholar
  36. Karami, K., Khaledian, M.S.: J. High Energy Phys. 03, 086 (2011)ADSCrossRefGoogle Scholar
  37. Li, M.: Phys. Lett. B 603, 1 (2004)ADSCrossRefGoogle Scholar
  38. Linder, E.V.: Phys. Rev. D 81, 127301 (2010)ADSCrossRefGoogle Scholar
  39. Linder, E.V.: Phys. Rev. D 81, 127301 (2010)ADSCrossRefGoogle Scholar
  40. Ling, Y., Pan, W.-J.: Mod. Phys. Lett. A 28, 1350128 (2013)ADSCrossRefGoogle Scholar
  41. Martin, J., Yamaguchi, M.: Phys. Rev. D 77, 123508 (2008)ADSCrossRefGoogle Scholar
  42. Meng, X., Du, X.: Phys. Lett. B 710, 493 (2012a)ADSCrossRefGoogle Scholar
  43. Meng, X., Du, X.: Commun. Theor. Phys. 57, 227 (2012b)ADSCrossRefGoogle Scholar
  44. Miessner, K.A.: Class. Quantum Gravity 21, 5245 (2004)ADSCrossRefGoogle Scholar
  45. Modak, S.K.: Phys. Lett. B 671, 167 (2009)ADSMathSciNetCrossRefGoogle Scholar
  46. Nojiri, S., Odintsov, S.D.: Phys. Lett. B 631, 1 (2005)ADSMathSciNetCrossRefGoogle Scholar
  47. Nojiri, S., Odintsov, S.D.: Phys. Lett. B 631, 1 (2005)ADSMathSciNetCrossRefGoogle Scholar
  48. Nojiri, S., Odintsov, S.D.: arXiv:0807.0685v1 [hep-th] (2008)
  49. Pavon, D., Zimdahl, W.: hep-th/0511053 (2005)
  50. Peebles, P.J.E., Ratra, B.: Astrophys. J. 325, L17 (1988)ADSCrossRefGoogle Scholar
  51. Perlmutter, S.J., et al.: Nature 391, 51 (1998)ADSCrossRefGoogle Scholar
  52. Radicella, N., Pavon, D.: Phys. Lett. B 691, 121 (2010)ADSCrossRefGoogle Scholar
  53. Rastkar, A.R., Setare, M.R., Darabi, F.: Astrophys. Space Sci. 337, 487 (2012)ADSCrossRefGoogle Scholar
  54. Riess, A.G., et al., Supernova Search Team Collaboration: Astron. J. 116, 1009 (1998)ADSCrossRefGoogle Scholar
  55. Sadjadi, H.M., Jamil, M.: Europhys. Lett. 92, 69001 (2010)ADSCrossRefGoogle Scholar
  56. Sen, A.: J. High Energy Phys. 0207, 065 (2002)ADSCrossRefGoogle Scholar
  57. Setare, M.R.: Int. J. Mod. Phys. D 12, 2219 (2008)ADSCrossRefGoogle Scholar
  58. Setare, M.R., Darabi, F.: arXiv:1110.3962v1 [physics.gen-ph] (2011)
  59. Setare, M.R., Jamil, M.: Europhys. Lett. 92, 49003 (2010)ADSCrossRefGoogle Scholar
  60. Setare, M.R., Saridakis, E.N.: Phys. Lett. B 670, 1 (2008)ADSCrossRefGoogle Scholar
  61. Sharif, M., Jawad, A.: Eur. Phys. J. C 73, 2382 (2013a)ADSCrossRefGoogle Scholar
  62. Sharif, M., Jawad, A.: Eur. Phys. J. C 73, 2600 (2013b)ADSCrossRefGoogle Scholar
  63. Sheykhi, A.: Phys. Lett. B 682, 329 (2010)ADSCrossRefGoogle Scholar
  64. Sheykhi, A., Jamil, M.: Gen. Relativ. Gravit. 43, 2661 (2011)ADSCrossRefGoogle Scholar
  65. Tsujikawa, S.: Lect. Notes Phys. 800, 99 (2010)ADSCrossRefGoogle Scholar
  66. Wald, R.M.: Phys. Rev. D 48, 3427 (1993)ADSMathSciNetCrossRefGoogle Scholar
  67. Wei, H.: Commun. Theor. Phys. 52, 743 (2009)ADSCrossRefGoogle Scholar
  68. Wei, H.: Class. Quantum Gravity 29, 175008 (2012)ADSCrossRefGoogle Scholar
  69. Wei, H., Zhang, S.N.: Phys. Rev. D 76, 063003 (2007)ADSCrossRefGoogle Scholar
  70. Wei, H., Cai, R.G., Zeng, D.F.: Class. Quantum Gravity 22, 3189 (2005)ADSCrossRefGoogle Scholar
  71. Yerzhanov, K.K., et al.: arXiv:1006.3879v1 [gr-qc] (2010)
  72. Zhang, X.: Int. J. Mod. Phys. D 14, 1597 (2005)ADSCrossRefGoogle Scholar
  73. Zlosnik, T.G., et al.: Phys. Rev. D 75, 044017 (2007)ADSCrossRefGoogle Scholar
  74. Zlosnik, T.G., Ferreira, P.G., Starkman, G.D.: Phys. Rev. D 75, 044017 (2007)ADSCrossRefGoogle Scholar
  75. Zuntz, J., et al.: Phys. Rev. D 81, 104015 (2010)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Engineering Science and TechnologyHowrahIndia

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