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Thermodynamics of apparent horizon in modified FRW universe with power-law corrected entropy

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Abstract

We derive the modified Friedmann equation corresponding to the power-law corrected entropy-area relation \( {S_A} = \frac{A}{4}\left[ {1 - {K_\alpha }{A^{1 - \frac{\alpha }{2}}}} \right] \) which is motivated by the entanglement of quantum fields in and out of the apparent horizon. We consider a non-flat modified FRW universe containing an interacting viscous dark energy with dark matter and radiation. For the selected model, we study the effect of the power-law correction term to the entropy on the dynamics of dark energy. Furthermore, we investigate the validity of the generalized second law (GSL) of gravitational thermodynamics on the apparent horizon and conclude that the GSL is satisfied for α < 2.

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References

  1. Supernova Search Team collaboration, A.G. Riess et al., Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant, Astron. J. 116 (1998) 1009 [astro-ph/9805201] [SPIRES].

    Article  ADS  Google Scholar 

  2. Supernova Cosmology Project collaboration, S. Perlmutter et al., Measurements of Omega and Lambda from 42 High-Redshift Supernovae, Astrophys. J. 517 (1999) 565 [astro-ph/9812133] [SPIRES].

    Article  ADS  Google Scholar 

  3. Boomerang collaboration, P. de Bernardis et al., A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation, Nature 404 (2000) 955 [astro-ph/0004404] [SPIRES].

    Article  Google Scholar 

  4. Supernova Cosmology Project collaboration, R.A. Knop et al., New Constraints on Ω M , ΩΛ and w from an Independent Set of Eleven High-Redshift Supernovae Observed with HST, Astrophys. J. 598 (2003) 102 [astro-ph/0309368] [SPIRES].

    Article  ADS  Google Scholar 

  5. T. Padmanabhan, Cosmological constant: The weight of the vacuum, Phys. Rept. 380 (2003) 235 [hep-th/0212290] [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. P.J.E. Peebles and B. Ratra, The cosmological constant and dark energy, Rev. Mod. Phys. 75 (2003) 559 [astro-ph/0207347] [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. E.J. Copeland, M. Sami and S. Tsujikawa, Dynamics of dark energy, Int. J. Mod. Phys. D 15 (2006) 1753 [hep-th/0603057] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  8. M. Li, X.-D. Li, S. Wang and Y. Wang, Dark Energy, arXiv:1103.5870 [SPIRES].

  9. S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  10. J.M. Bardeen, B. Carter and S.W. Hawking, The Four laws of black hole mechanics, Commun. Math. Phys. 31 (1973) 161 [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. T. Jacobson, Thermodynamics of space-time: The Einstein equation of state, Phys. Rev. Lett. 75 (1995) 1260 [gr-qc/9504004] [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. R.-G. Cai and S.P. Kim, First law of thermodynamics and Friedmann equations of Friedmann-Robertson-Walker universe, JHEP 02 (2005) 050 [hep-th/0501055] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  13. M. Akbar and R.-G. Cai, Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe, Phys. Rev. D 75 (2007) 084003 [hep-th/0609128] [SPIRES].

    ADS  Google Scholar 

  14. A. Sheykhi, Thermodynamical interpretation of gravity in braneworld scenarios, JCAP 05 (2009) 019 [SPIRES].

    ADS  Google Scholar 

  15. R. Banerjee and B.R. Majhi, Quantum Tunneling and Back Reaction, Phys. Lett. B 662 (2008) 62 [arXiv:0801.0200] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  16. R. Banerjee and B.R. Majhi, Quantum Tunneling Beyond Semiclassical Approximation, JHEP 06 (2008) 095 [arXiv:0805.2220] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  17. R. Biswas, N. Mazumder and S. Chakraborty, Hawking-like radiation from the apparent horizon in an FRW Universe: Quantum Corrections, arXiv:1106.4370 [SPIRES].

  18. R. Banerjee and S.K. Modak, Exact Differential and Corrected Area Law for Stationary Black Holes in Tunneling Method, JHEP 05 (2009) 063 [arXiv:0903.3321] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  19. S.K. Modak, Corrected entropy of BTZ black hole in tunneling approach, Phys. Lett. B 671 (2009) 167 [arXiv:0807.0959] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  20. R. Banerjee, S. Gangopadhyay and S.K. Modak, Voros product, Noncommutative Schwarzschild Black Hole and Corrected Area Law, Phys. Lett. B 686 (2010) 181 [arXiv:0911.2123] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  21. S. Das, S. Shankaranarayanan and S. Sur, Power-law corrections to entanglement entropy of black holes, Phys. Rev. D 77 (2008) 064013 [arXiv:0705.2070] [SPIRES].

    ADS  Google Scholar 

  22. G. Izquierdo and D. Pavon, The generalized second law in phantom dominated universes in the presence of black holes, Phys. Lett. B 639 (2006) 1 [gr-qc/0606014] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  23. H. Mohseni Sadjadi, Generalized second law in phantom dominated universe, Phys. Rev. D 73 (2006) 063525 [gr-qc/0512140] [SPIRES].

    ADS  Google Scholar 

  24. H. Mohseni Sadjadi, Generalized second law in modified theory of gravity, Phys. Rev. D 76 (2007) 104024 [arXiv:0709.2435] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  25. H. Mohseni Sadjadi, Schwarzschild black hole and the generalized second law in phantom-dominated universe, Phys. Lett. B 645 (2007) 108 [gr-qc/0611114] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  26. J. Zhou, B. Wang, Y. Gong and E. Abdalla, The second law of thermodynamics in the accelerating universe, Phys. Lett. B 652 (2007) 86 [arXiv:0705.1264] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  27. Y. Gong, B. Wang and A. Wang, On thermodynamical properties of dark energy, Phys. Rev. D 75 (2007) 123516 [gr-qc/0611155] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  28. Y. Gong, B. Wang and A. Wang, Thermodynamical properties of the universe with dark energy, JCAP 01 (2007) 024 [gr-qc/0610151] [SPIRES].

    ADS  Google Scholar 

  29. A. Sheykhi and B. Wang, The generalized second law of thermodynamics in Gauss-Bonnet braneworld, Phys. Lett. B 678 (2009) 434 [arXiv:0811.4478] [SPIRES].

    ADS  Google Scholar 

  30. A. Sheykhi and B. Wang, Generalized second law of thermodynamics in warped DGP braneworld, Mod. Phys. Lett. A 25 (2010) 1199 [arXiv:0811.4477] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  31. A. Sheykhi, Entropic Corrections to Friedmann Equations, Phys. Rev. D 81 (2010) 104011 [arXiv:1004.0627] [SPIRES].

    ADS  Google Scholar 

  32. A. Sheykhi, Thermodynamics of apparent horizon and modified Friedmann equations, Eur. Phys. J. C 69 (2010) 265 [arXiv:1012.0383] [SPIRES].

    Article  ADS  Google Scholar 

  33. A. Sheykhi, Thermodynamics of interacting holographic dark energy with apparent horizon as an IR cutoff, Class. Quant. Grav. 27 (2010) 025007 [arXiv:0910.0510] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  34. K. Karami, Comment on “Interacting holographic dark energy model and generalized second law of thermodynamics in a non-flat universe”, by M.R. Setare (JCAP 01 (2007) 023, JCAP 01 (2010) 015 [arXiv:0911.4808] [SPIRES].

    ADS  Google Scholar 

  35. K. Karami and S. Ghaffari, The generalized second law of thermodynamics for the interacting dark energy in a non-flat FRW universe enclosed by the apparent and event horizons, Phys. Lett. B 685 (2010) 115 [arXiv:0912.0363] [SPIRES].

    ADS  Google Scholar 

  36. K. Karami and S. Ghaffari, The generalized second law of thermodynamics for the interacting polytropic dark energy in non-flat FRW universe enclosed by the apparent horizon, Phys. Lett. B 688 (2010) 125 [SPIRES].

    ADS  Google Scholar 

  37. K. Karami, S. Ghaffari and M.M. Soltanzadeh, The generalized second law of gravitational thermodynamics on the apparent and event horizons in FRW cosmology, Class. Quant. Grav. 27 (2010) 205021 [arXiv:1101.3240] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  38. K. Karami and A. Abdolmaleki, The generalized second law for the interacting new agegraphic dark energy in a non-flat FRW universe enclosed by the apparent horizon, Astrophys. Space Sci. 331 (2011) 309 [arXiv:0909.2427] [SPIRES].

    Article  ADS  Google Scholar 

  39. N. Radicella and D. Pavón, The generalized second law in universes with quantum corrected entropy relations, Phys. Lett. B 691 (2010) 121 [arXiv:1006.3745] [SPIRES].

    ADS  Google Scholar 

  40. J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [SPIRES].

    ADS  MathSciNet  Google Scholar 

  41. P.C.W. Davies, Cosmological horizons and the generalized second law of thermodynamics, Class. Quant. Grav. 4 (1987) L225 [SPIRES].

    Article  ADS  Google Scholar 

  42. G. Izquierdo and D. Pavón, Dark energy and the generalized second law, Phys. Lett. B 633 (2006) 420 [astro-ph/0505601] [SPIRES].

    ADS  Google Scholar 

  43. B. Wang, Y. Gong and E. Abdalla, Thermodynamics of an accelerated expanding universe, Phys. Rev. D 74 (2006) 083520 [gr-qc/0511051] [SPIRES].

    ADS  Google Scholar 

  44. J. Ren and X.-H. Meng, Cosmological model with viscosity media (dark fluid) described by an effective equation of state, Phys. Lett. B 633 (2006) 1 [astro-ph/0511163] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  45. E. Poisson and W. Israel, Internal structure of black holes, Phys. Rev. D 41 (1990) 1796 [SPIRES].

    ADS  MathSciNet  Google Scholar 

  46. S.A. Hayward, Gravitational energy in spherical symmetry, Phys. Rev. D 53 (1996) 1938 [gr-qc/9408002] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  47. Y. Gong and A. Wang, The Friedmann equations and thermodynamics of apparent horizons, Phys. Rev. Lett. 99 (2007) 211301 [arXiv:0704.0793] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  48. R.G. Cai, L.M. Cao and Y.P. Hu, Hawking Radiation of Apparent Horizon in a FRW Universe, Class. Quant. Grav. 26 (2009) 155018 [arXiv:0809.1554] [SPIRES].

    Article  ADS  Google Scholar 

  49. R.-G. Cai, L.-M. Cao and Y.-P. Hu, Corrected Entropy-Area Relation and Modified Friedmann Equations, JHEP 08 (2008) 090 [arXiv:0807.1232] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  50. I.H. Brevik and O. Gorbunova, Dark Energy and Viscous Cosmology, Gen. Rel. Grav. 37 (2005) 2039 [gr-qc/0504001] [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  51. I.H. Brevik, O. Gorbunova and Y.A. Shaido, Viscous FRW cosmology in modified gravity, Int. J. Mod. Phys. D 14 (2005) 1899 [gr-qc/0508038] [SPIRES].

    ADS  Google Scholar 

  52. I.H. Brevik and O. Gorbunova, Viscous Dark Cosmology with Account of Quantum Effects, Eur. Phys. J. C 56 (2008) 425 [arXiv:0806.1399] [SPIRES].

    Article  ADS  Google Scholar 

  53. J. Ren and X.-H. Meng, Modified equation of state, scalar field and bulk viscosity in Friedmann universe, Phys. Lett. B 636 (2006) 5 [astro-ph/0602462] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  54. A. Sheykhi and M.R. Setare, Interacting new agegraphic viscous dark energy with varying G, Int. J. Theor. Phys. 49 (2010) 2777 [arXiv:1003.1109] [SPIRES].

    Article  MATH  MathSciNet  Google Scholar 

  55. N. Cruz, S. Lepe and F. Pena, The coincidence problem in the scenario of dark energy interacting with two fluids, arXiv:0910.1307 [SPIRES].

  56. M. Jamil, F. Rahaman and M. Kalam, Cosmic coincidence problem and variable constants of physics, Eur. Phys. J. C 60 (2009) 149 [arXiv:0809.4314] [SPIRES].

    Article  ADS  Google Scholar 

  57. M. Jamil and F. Rahaman, On the resolution of cosmic coincidence problem and phantom crossing with triple interacting fluids, Eur. Phys. J. C 64 (2009) 97 [SPIRES].

    Article  ADS  Google Scholar 

  58. M. Jamil, E.N. Saridakis and M.R. Setare, Thermodynamics of dark energy interacting with dark matter and radiation, Phys. Rev. D 81 (2010) 023007 [arXiv:0910.0822] [SPIRES].

    ADS  Google Scholar 

  59. G. ’t Hooft, Dimensional reduction in quantum gravity, gr-qc/9310026 [SPIRES].

  60. L. Susskind, The World as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  61. M. Li, A model of holographic dark energy, Phys. Lett. B 603 (2004) 1 [hep-th/0403127] [SPIRES].

    ADS  Google Scholar 

  62. Q.-G. Huang and M. Li, The holographic dark energy in a non-flat universe, JCAP 08 (2004) 013 [astro-ph/0404229] [SPIRES].

    ADS  Google Scholar 

  63. A. Sheykhi and M. Jamil, Power-Law Entropy Corrected Holographic Dark Energy Model, arXiv:1011.0134 [SPIRES].

  64. G. Dvali and M.S. Turner, Dark energy as a modification of the Friedmann equation, astro-ph/0301510 [SPIRES].

  65. S.D.H. Hsu, Entropy bounds and dark energy, Phys. Lett. B 594 (2004) 13 [hep-th/0403052] [SPIRES].

    ADS  Google Scholar 

  66. M. Li, X.-D. Li, S. Wang and X. Zhang, Holographic dark energy models: A comparison from the latest observational data, JCAP 06 (2009) 036 [arXiv:0904.0928] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  67. WMAP collaboration, E. Komatsu et al., Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation, Astrophys. J. Suppl. 192 (2011) 18 [arXiv:1001.4538] [SPIRES].

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of Kurdistan, Pasdaran St., Sanandaj, Iran

    K. Karami, A. Abdolmaleki, N. Sahraei & S. Ghaffari

  2. Research Institute for Astronomy & Astrophysics of Maragha (RIAAM), Maragha, Iran

    K. Karami

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  1. K. Karami
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ArXiv ePrint: 1009.3833

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Karami, K., Abdolmaleki, A., Sahraei, N. et al. Thermodynamics of apparent horizon in modified FRW universe with power-law corrected entropy. J. High Energ. Phys. 2011, 150 (2011). https://doi.org/10.1007/JHEP08(2011)150

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