The generalized second law of thermodynamics in Ho¡rava-Lifshitz cosmology

Journal of Cosmology and Astroparticle Physics

Volumn 2010, Issue 11, 2010, Pages

  Jamil, Mubasher ^a   Saridakis, Emmanuel N ^b   Setare, M R ^c  

^a NATIONAL UNIVERSITY OF SCIENCES AND TECHNOLOGY   (Pakistan)

^b UNIVERSITY OF ATHENS   (Greece)

^c UNIVERSITY OF KURDISTAN   (Iran)

Author keywords

Gravity; Modified gravity

Indexed keywords

EID: 78649831461     PISSN: 14757516     EISSN: 14757516     Source Type: Journal    
DOI: 10.1088/1475-7516/2010/11/032     Document Type: Article

References (175)

1. P. Hǒrava, Quantum criticality and Yang-Mills gauge theory, Phys. Lett. B 694 (2010) 172 [arXiv:0811.2217] [SPIRES].
2. P. Hǒrava, Membranes at quantum criticality, JHEP 03 (2009) 020 [arXiv:0812.4287] [SPIRES].
3. P. Hǒrava, Quantum gravity at a Lifshitz point, Phys. Rev. D 79 (2009) 084008 [arXiv:0901.3775] [SPIRES].
4. P. Hǒrava, Spectral dimension of the universe in quantum gravity at a Lifshitz point, Phys. Rev. Lett. 102 (2009) 161301 [arXiv:0902.3657] [SPIRES].
5. G.E. Volovik, z = 3 Lifshitz-Hǒrava model and Fermi-point scenario of emergent gravity, JETP Lett. 89 (2009) 525 [arXiv:0904.4113] [SPIRES].
6. R.-G. Cai, Y. Liu and Y.-W. Sun, On the z = 4 Hǒrava-Lifshitz gravity, JHEP 06 (2009) 010 [arXiv:0904.4104] [SPIRES].
7. R.-G. Cai, B. Hu and H.-B. Zhang, Dynamical scalar degree offreedom in Hǒrava-Lifshitz gravity, Phys. Rev. D 80 (2009) 041501 [arXiv:0905.0255] [SPIRES].
8. D. Orlando and S. Reffert, On the renormalizability ofHǒrava- Lifshitz-type gravities, Class. Quant. Grav. 26 (2009) 155021 [arXiv:0905.0301] [SPIRES].
9. T. Nishioka, Hǒrava-Lifshitz holography, Class. Quant. Grav. 26 (2009) 242001 [arXiv:0905.0473] [SPIRES].
10. R.A. Konoplya, Towards constraining of the Hǒrava-Lifshitz gravities, Phys. Lett. B 679 (2009) 499 [arXiv:0905.1523] [SPIRES].
11. C. Charmousis, G. Niz, A. Padilla and P.M. Saffin, Strong coupling in Hǒrava gravity, JHEP 08 (2009) 070 [arXiv:0905.2579] [SPIRES].
12. T.P. Sotiriou, M. Visser and S. Weinfurtner, Phenomenologically viable Lorentz-violating quantum gravity, Phys. Rev. Lett. 102 (2009) 251601 [arXiv:0904.4464] [SPIRES].
13. T.P. Sotiriou, M. Visser and S. Weinfurtner, Quantum gravity without Lorentz invariance, JHEP 10 (2009) 033 [arXiv:0905.2798] [SPIRES].
14. C. Germani, A. Kehagias and K. Sfetsos, Relativistic quantum gravity at a Lifshitz point, JHEP 09 (2009) 060 [arXiv:0906.1201] [SPIRES].
15. C. Bogdanos and E.N. Saridakis, Perturbative instabilities in Hǒrava gravity, Class. Quant. Grav. 27 (2010) 075005 [arXiv:0907.1636] [SPIRES].
16. J. Kluson, Hǒrava-Lifshitz f(R) gravity, JHEP 11 (2009) 078 [arXiv:0907.3566] [SPIRES].
17. N. Afshordi, Cuscuton and low energy limit ofHǒrava-Lifshitz gravity, Phys. Rev. D 80 (2009) 081502 [arXiv:0907.5201] [SPIRES].
18. Y.S. Myung, Generalized uncertainty principle and Hǒrava-Lifshitz gravity, Phys. Lett. B 679 (2009) 491 [arXiv:0907.5256] [SPIRES].
19. J. Alexandre, K. Farakos, P. Pasipoularides and A. Tsapalis, Schwinger-Dyson approach for a Lifshitz-type Yukawa model, Phys. Rev. D 81 (2010) 045002 [arXiv:0909.3719] [SPIRES].
20. D. Blas, O. Pujol̀as and S. Sibiryakov, Consistent extension of Hǒrava gravity, Phys. Rev. Lett. 104 (2010) 181302 [arXiv:0909.3525] [SPIRES].
21. D. Capasso and A.P. Polychronakos, Particle kinematics in Hǒrava-Lifshitz gravity, JHEP 02 (2010) 068 [arXiv:0909.5405] [SPIRES].
22. B. Chen, S. Pi and J.-Z. Tang, Power spectra of scalar and tensor modes in modified Hǒrava-Lifshitz gravity, arXiv:0910.0338 [SPIRES].
23. S. Nojiri and S.D. Odintsov, Covariant Hǒrava-like renormalizable gravity and its FRW cosmology, Phys. Rev. D 81 (2010) 043001 [arXiv:0905.4213] [SPIRES].
24. K. Koyama and F. Arroja, Pathological behaviour of the scalar graviton in Hǒrava-Lifshitz gravity, JHEP 03 (2010) 061 [arXiv:0910.1998] [SPIRES].
25. A. Papazoglou and T.P. Sotiriou, Strong coupling in extended Hǒrava-Lifshitz gravity, Phys. Lett. B 685 (2010) 197 [arXiv:0911.1299] [SPIRES].
26. J. Kluson, New models off(R) theories ofgravity, Phys. Rev. D 81 (2010) 064028 [arXiv:0910.5852] [SPIRES].
27. J. Kluson, String in Hǒrava-Lifshitz gravity, Phys. Rev. D 82 (2010) 086007 [arXiv:1002.2849] [SPIRES].
28. M. Li and Y. Pang, A trouble with Hǒrava-Lifshitz gravity, JHEP 08 (2009) 015 [arXiv:0905.2751] [SPIRES].
29. J. Chen and Y. Wang, Timelike geodesic motion in Hǒrava-Lifshitz spacetime, Int. J. Mod. Phys. A 25 (2010) 1439 [arXiv:0905.2786] [SPIRES].
30. B. Chen and Q.-G. Huang, Field theory at a Lifshitzpoint, Phys. Lett. B 683 (2010) 108 [arXiv:0904.4565] [SPIRES].
31. F.-W. Shu and Y.-S. Wu, Stochastic quantization of the Hǒrava gravity, arXiv:0906.1645 [SPIRES].
32. G. Calcagni, Cosmology of the Lifshitz universe, JHEP 09 (2009) 112 [arXiv:0904.0829] [SPIRES].
33. E. Kiritsis and G. Kofinas, Hǒrava-Lifshitz cosmology, Nucl. Phys. B 821 (2009) 467 [arXiv:0904.1334] [SPIRES].
34. H. Lü, J. Mei and C.N. Pope, Solutions to Hǒrava gravity, Phys. Rev. Lett. 103 (2009) 091301 [arXiv:0904.1595] [SPIRES].
35. H. Nastase, On IR solutions in Hǒrava gravity theories, arXiv:0904.3604 [SPIRES].
36. E. O Colgain and H. Yavartanoo, Dyonic solution ofHǒrava-Lifshitz gravity, JHEP 08 (2009) 021 [arXiv:0904.4357] [SPIRES].
37. A. Ghodsi, Toroidal solutions in Hǒrava gravity, arXiv:0905.0836 [SPIRES].
38. M. Minamitsuji, Classification of cosmology with arbitrary matter in the Hǒrava-Lifshitz theory, Phys. Lett. B 684 (2010) 194 [arXiv:0905.3892] [SPIRES].
39. A. Ghodsi and E. Hatefi, Extremal rotating solutions in Hǒrava gravity, Phys. Rev. D 81 (2010) 044016 [arXiv:0906.1237] [SPIRES].
40. P. Wu and H.W. Yu, Emergent universe from the Hǒrava-Lifshitz gravity, Phys. Rev. D 81 (2010) 103522 [arXiv:0909.2821] [SPIRES].
41. I. Cho and G. Kang, Four dimensional string solutions in Hǒrava-Lifshitz gravity, JHEP 07 (2010) 034 [arXiv:0909.3065] [SPIRES].
42. C.G. Boehmer and F.S.N. Lobo, Stability of the Einstein static universe in IR modified Hǒrava gravity, arXiv:0909.3986 [SPIRES].
43. D. Momeni, Cylindrical solutions in a non-relativistic quantum gravity, arXiv:0910.0594 [SPIRES].
44. M.R. Setare and D. Momeni, Plane symmetric solutions in Hǒrava-Lifshitz theory, Int. J. Mod. Phys. D 19 (2010) 2079 [arXiv:0911.1877] [SPIRES].
45. E. Kiritsis, Spherically symmetric solutions in modified Hǒrava-Lifshitz gravity, Phys. Rev. D 81 (2010) 044009 [arXiv:0911.3164] [SPIRES].
46. R.-G. Cai and A. Wang, Singularities in Hǒrava-Lifshitz theory, Phys. Lett. B 686 (2010) 166 [arXiv:1001.0155] [SPIRES].
47. M. Chaichian, S. Nojiri, S.D. Odintsov, M. Oksanen and A. Tureanu, Modified f(R) Hǒrava-Lifshitz gravity: a way to accelerating FRW cosmology, Class. Quant. Grav. 27 (2010) 185021 [arXiv:1001.4102] [SPIRES].
48. S. Carloni, E. Elizalde and P.J. Silva, An analysis of the phase space ofHǒrava-Lifshitz cosmologies, Class. Quant. Grav. 27 (2010) 045004 [arXiv:0909.2219] [SPIRES].
49. G. Leon and E.N. Saridakis, Phase-space analysis ofHǒrava-Lifshitz cosmology, JCAP 11 (2009) 006 [arXiv:0909.3571] [SPIRES].
50. Y.S. Myung, Y.-W. Kim, W.-S. Son and Y.-J. Park, Chaotic universe in the z = 2 Hovava-Lifshitz gravity, Phys. Rev. D 82 (2010) 043506 [arXiv:0911.2525] [SPIRES].
51. I. Bakas, F. Bourliot, D. Lüst and M. Petropoulos, Mixmaster universe in Hǒrava-Lifshitz gravity, Class. Quant. Grav. 27 (2010) 045013 [arXiv:0911.2665] [SPIRES].
52. Y.S. Myung, Y.-W. Kim, W.-S. Son and Y.-J. Park, Mixmaster universe in the z = 3 deformed Hǒrava-Lifshitz gravity, JHEP 03 (2010) 085 [arXiv:1001.3921] [SPIRES].
53. S. Mukohyama, K. Nakayama, F. Takahashi and S. Yokoyama, Phenomenological aspects of Hǒrava-Lifshitz cosmology, Phys. Lett. B 679 (2009) 6 [arXiv:0905.0055] [SPIRES].
54. T. Takahashi and J. Soda, Chiral primordial gravitational waves from a Lifshitz point, Phys. Rev. Lett. 102 (2009) 231301 [arXiv:0904.0554] [SPIRES].
55. S. Koh, Relic gravitational wave spectrum, the trans-Planckian physics and Hǒrava-Lifshitz gravity, Class. Quant. Grav. 27 (2010) 225015 [arXiv:0907.0850] [SPIRES].
56. M.-I. Park, Remarks on the scalar graviton decoupling and consistency of Hǒrava gravity, arXiv:0910.1917 [SPIRES].
57. M.-I. Park, Hǒrava gravity and gravitons at a conformalpoint, arXiv:0910.5117 [SPIRES].
58. Y.S. Myung, Chiral gravitational waves from z = 2 Hǒrava-Lifshitz gravity, Phys. Lett. B 684 (2010) 1 [arXiv:0911.0724] [SPIRES].
59. S. Mukohyama, Scale-invariant cosmological perturbations from Hǒrava-Lifshitz gravity without inflation, JCAP 06 (2009) 001 [arXiv:0904.2190] [SPIRES].
60. Y.-S. Piao, Primordial perturbation in Hǒrava-Lifshitz cosmology, Phys. Lett. B 681 (2009) 1 [arXiv:0904.4117] [SPIRES].
61. X. Gao, Cosmological perturbations and non-Gaussianities in Hǒrava-Lifshitz gravity, arXiv:0904.4187 [SPIRES].
62. B. Chen, S. Pi and J.-Z. Tang, Scale invariant power spectrum in Hǒrava-Lifshitz cosmology without matter, JCAP 08 (2009) 007 [arXiv:0905.2300] [SPIRES].
63. X. Gao, Y. Wang, R. Brandenberger and A. Riotto, Cosmological perturbations in Hǒrava-Lifshitz gravity, Phys. Rev. D 81 (2010) 083508 [arXiv:0905.3821] [SPIRES].
64. Y.-F. Cai and X. Zhang, Primordial perturbation with a modified dispersion relation, Phys. Rev. D 80 (2009) 043520 [arXiv:0906.3341] [SPIRES].
65. A. Wang and R. Maartens, Linear perturbations of cosmological models in the Hǒrava-Lifshitz theory ofgravity without detailed balance, Phys. Rev. D 81 (2010) 024009 [arXiv:0907.1748] [SPIRES].
66. T. Kobayashi, Y. Urakawa and M. Yamaguchi, Large scale evolution of the curvature perturbation in Hǒrava-Lifshitz cosmology, JCAP 11 (2009) 015 [arXiv:0908.1005] [SPIRES].
67. A. Wang, D. Wands and R. Maartens, Scalar field perturbations in Hǒrava-Lifshitz cosmology, JCAP 03 (2010) 013 [arXiv:0909.5167] [SPIRES].
68. T. Kobayashi, Y. Urakawa and M. Yamaguchi, Cosmological perturbations in a healthy extension of Hǒrava gravity, JCAP 04 (2010) 025 [arXiv:1002.3101] [SPIRES].
69. R. Brandenberger, Matter bounce in Hǒrava-Lifshitz cosmology, Phys. Rev. D 80 (2009) 043516 [arXiv:0904.2835] [SPIRES].
70. R.H. Brandenberger, Processing of cosmological perturbations in a cyclic cosmology, Phys. Rev. D 80 (2009) 023535 [arXiv:0905.1514] [SPIRES].
71. Y.-F. Cai and E.N. Saridakis, Non-singular cosmology in a model of non-relativistic gravity, JCAP 10 (2009) 020 [arXiv:0906.1789] [SPIRES].
72. T. Suyama, Notes on matter in Hǒrava-Lifshitz gravity, arXiv:0909.4833 [SPIRES].
73. E. Czuchry, The phase portrait of a matter bounce in Hǒrava- Lifshitz cosmology, arXiv:0911.3891 [SPIRES].
74. X. Gao, Y. Wang, W. Xue and R. Brandenberger, Fluctuations in a Hǒrava-Lifshitz bouncing cosmology, JCAP 02 (2010) 020 [arXiv:0911.3196] [SPIRES].
75. E.N. Saridakis, Hǒrava-Lifshitz dark energy, Eur. Phys. J. C 67 (2010) 229 [arXiv:0905.3532] [SPIRES].
76. M.-I. Park, A test of Hǒrava gravity: the dark energy, JCAP 01 (2010) 001 [arXiv:0906.4275] [SPIRES].
77. C. Appignani, R. Casadio and S. Shankaranarayanan, The cosmological constant and Hǒrava-Lifshitz gravity, JCAP 04 (2010) 006 [arXiv:0907.3121] [SPIRES].
78. M.R. Setare, Interacting dark energy in Hǒrava-Lifshitz cosmology, arXiv:0909.0456 [SPIRES].
79. R. Garattini, The cosmological constant as an eigenvalue of the Hamiltonian constraint in Hǒrava-Lifshits theory, arXiv:0912.0136 [SPIRES].
80. M.R. Setare and M. Jamil, Holographic dark energy with varying gravitational constant in Hǒrava-Lifshitz cosmology, JCAP 02 (2010) 010
81. [Erratum ibid. 08 (2010) E01] [arXiv:1001.1251] [SPIRES].
82. M. Jamil and E.N. Saridakis, New agegraphic dark energy in Hǒrava-Lifshitz cosmology, JCAP 07 (2010) 028 [arXiv:1003.5637] [SPIRES].
83. S.-S. Kim, T. Kim and Y. Kim, Surplus solid angle: toward astrophysical test of Hǒrava-Lifshitz gravity, Phys. Rev. D 80 (2009) 124002 [arXiv:0907.3093] [SPIRES].
84. L. Iorio and M.L. Ruggiero, Phenomenological constraints on the Kehagias-Sfetsos solution in the Hǒrava-Lifshitz gravity from solar system orbital motions, arXiv:0909.2562 [SPIRES].
85. L. Iorio and M.L. Ruggiero, Constraining the Kehagias-Sfetsos solution in the Hǒrava-Lifshitz gravity with extrasolarplanets, arXiv:0909.5355 [SPIRES].
86. K. Izumi and S. Mukohyama, Stellar center is dynamical in Hǒrava-Lifshitz gravity, Phys. Rev. D 81 (2010) 044008 [arXiv:0911.1814] [SPIRES].
87. T. Harko, Z. Kovacs and F.S.N. Lobo, Solar system tests ofHǒrava-Lifshitz gravity, arXiv:0908.2874 [SPIRES].
88. S. Dutta and E.N. Saridakis, Observational constraints on Hǒrava-Lifshitz cosmology, JCAP 01 (2010) 013 [arXiv:0911.1435] [SPIRES].
89. S. Dutta and E.N. Saridakis, Overall observational constraints on the running parameter a; of Hǒrava-Lifshitz gravity, JCAP 05 (2010) 013 [arXiv:1002.3373] [SPIRES].
90. A. Ali, S. Dutta, E.N. Saridakis and A.A. Sen, Hǒrava-Lifshitz cosmology with generalized Chaplygin gas, arXiv:1004.2474 [SPIRES].
91. U.H. Danielsson and L. Thorlacius, Black holes in asymptotically Lifshitz spacetime, JHEP 03 (2009) 070 [arXiv:0812.5088] [SPIRES].
92. R.-G. Cai, L.-M. Cao and N. Ohta, Topological black holes in Hǒrava-Lifshitz gravity, Phys. Rev. D 80 (2009) 024003 [arXiv:0904.3670] [SPIRES].
93. Y.S. Myung and Y.-W. Kim, Thermodynamics ofHǒrava-Lifshitz black holes, Eur. Phys. J. C 68 (2010) 265 [arXiv:0905.0179] [SPIRES].
94. A. Kehagias and K. Sfetsos, The black hole and FRWgeometries ofnon-relativistic gravity, Phys. Lett. B 678 (2009) 123 [arXiv:0905.0477] [SPIRES].
95. R.B. Mann, Lifshitz topological black holes, JHEP 06 (2009) 075 [arXiv:0905.1136] [SPIRES].
96. G. Bertoldi, B.A. Burrington and A. Peet, Black holes in asymptotically Lifshitz spacetimes with arbitrary critical exponent, Phys. Rev. D 80 (2009) 126003 [arXiv:0905.3183] [SPIRES].
97. M.-I. Park, The black hole and cosmological solutions in IR modified Hǒrava gravity, JHEP 09 (2009) 123 [arXiv:0905.4480] [SPIRES].
98. A. Castillo and A. Larranaga, Entropy for black holes in the deformed Hǒrava-Lifshitz gravity, arXiv:0906.4380 [SPIRES].
99. M. Botta-Cantcheff, N. Grandi and M. Sturla, Wormhole solutions to Hǒrava gravity, arXiv:0906.0582 [SPIRES].
100. H.W. Lee, Y.-W. Kim and Y.S. Myung, Extremal black holes in the Hǒrava-Lifshitz gravity, Eur. Phys. J. C 68 (2010) 255 [arXiv:0907.3568] [SPIRES].
101. N. Varghese and V.C. Kuriakose, Stability of black holes in Hǒrava gravity: gravitational quasinormal modes, arXiv:0909.4944 [SPIRES].
102. E. Kiritsis and G. Kofinas, On Hǒrava-Lifshitz 'black holes', JHEP 01 (2010) 122 [arXiv:0910.5487] [SPIRES].
103. B.R. Majhi, Hawking radiation and black hole spectroscopy in Hǒrava-Lifshitz gravity, Phys. Lett. B 686 (2010) 49 [arXiv:0911.3239] [SPIRES].
104. J. Greenwald, A. Papazoglou and A. Wang, Black holes and stars in Hǒrava-Lifshitz theory withprojectability condition, Phys. Rev. D 81 (2010) 084046 [arXiv:0912.0011] [SPIRES].
105. M.R. Setare and D. Momeni, Geodesic stability for KS black hole in Hǒrava-Lifshitz gravity via Lyapunov exponents, arXiv:1001.3767 [SPIRES].
106. M.R. Setare and M. Jamil, Cardy-Verlinde formula ofKehagias-Sfetsos black hole, arXiv:1001.4716 [SPIRES].
107. F.S.N. Lobo, T. Harko and Z. Kovacs, Solar system tests ofHǒrava-Lifshitz black holes, arXiv:1001.3517 [SPIRES].
108. M.R. Setare and D. Momeni, Spacing of the entropy spectrum for KS black hole in Hǒrava-Lifshitz gravity, arXiv:1002.0185 [SPIRES].
109. R.-G. Cai, L.-M. Cao and N. Ohta, Thermodynamics of black holes in Hǒrava-Lifshitz gravity, Phys. Lett. B 679 (2009) 504 [arXiv:0905.0751] [SPIRES].
110. R.-G. Cai and N. Ohta, Horizon thermodynamics and gravitational field equations in Hǒrava-Lifshitz gravity, Phys. Rev. D 81 (2010) 084061 [arXiv:0910.2307] [SPIRES].
111. Y.S. Myung, Thermodynamics of black holes in the deformed Hǒrava-Lifshitz gravity, Phys. Lett. B 678 (2009) 127 [arXiv:0905.0957] [SPIRES].
112. S.-W. Wei, Y.-X. Liu, Y.-Q. Wang and H. Guo, Thermodynamic geometry of black hole in the deformed Hǒrava-Lifshitz gravity, arXiv:1002.1550 [SPIRES].
113. T. Padmanabhan, Thermodynamical aspects ofgravity: new insights, Rept. Prog. Phys. 73 (2010) 046901 [arXiv:0911.5004] [SPIRES].
114. T. Padmanabhan, Entropy density of spacetime and thermodynamic interpretation of field equations ofgravity in any diffeomorphism invariant theory, arXiv:0903.1254 [SPIRES].
115. D. Bak and S.-J. Rey, Cosmic holography, Class. Quant. Grav. 17 (2000) L83 [hep-th/9902173] [SPIRES].
116. A. Wang and Y. Wu, Thermodynamics and classification of cosmological models in the Hǒrava-Lifshitz theory of gravity, JCAP 07 (2009) 012 [arXiv:0905.4117] [SPIRES].
117. Q.-J. Cao, Y.-X. Chen and K.-N. Shao, Clausius relation and Friedmann equation in FRW universe model, JCAP 05 (2010) 030 [arXiv:1001.2597] [SPIRES].
118. F.-W. Shu and Y. Gong, Equipartition of energy and the first law of thermodynamics at the apparent horizon, arXiv:1001.3237 [SPIRES].
119. S.-W. Wei, Y.-X. Liu and Y.-Q. Wang, Friedmann equation ofFRWuniverse in deformed Hǒrava-Lifshitz gravity from entropic force, arXiv: 1001. 5238 [SPIRES].
120. Y. Zhang, Y.-g. Gong and Z.-H. Zhu, Modified gravity emerging from thermodynamics and holographicprinciple, arXiv:1001.4677 [SPIRES].
121. A. Paranjape, S. Sarkar and T. Padmanabhan, Thermodynamic route to field equations in Lancos-Lovelockgravity, Phys. Rev. D 74 (2006) 104015 [hep-th/0607240] [SPIRES].
122. S.M. Carroll and E.A. Lim, Lorentz-violating vectorfields slow the universe down, Phys. Rev. D 70 (2004) 123525 [hep-th/0407149] [SPIRES].
123. W.G. Unruh and R.M. Wald, Acceleration radiation and generalized second law of thermodynamics, Phys. Rev. D 25 (1982) 942 [SPIRES].
124. P.C.W. Davies, Cosmological horizons and the generalized second law ofthermodynamics, Class. Quant. Grav. 4 (1987) L225 [SPIRES].
125. H. Mohseni Sadjadi, Generalized second law in modified theory ofgravity, Phys. Rev. D 76 (2007) 104024 [arXiv:0709.2435] [SPIRES].
126. R. Horvat, Renormalization-group running cosmologies and the generalized second law, Phys. Lett. B 648 (2007) 374 [gr-qc/0702087] [SPIRES].
127. 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].
128. S.-F. Wu, B. Wang, G.-H. Yang and P.-M. Zhang, The generalized second law of thermodynamics in generalized gravity theories, Class. Quant. Grav. 25 (2008) 235018 [arXiv:0801.2688] [SPIRES].
129. A. Sheykhi and B. Wang, The generalized second law ofthermodynamics in Gauss-Bonnet braneworld, Phys. Lett. B 678 (2009) 434 [arXiv:0811.4478] [SPIRES].
130. E.N. Saridakis, P.F. Gonzalez-Diaz and C.L. Siguenza, Unified dark energy thermodynamics: varying w and the\1-crossing, Class. Quant. Grav. 26 (2009) 165003 [arXiv:0901.1213] [SPIRES].
131. A.C. Wall, Tenproofs of the generalized second law, JHEP 06 (2009) 021 [arXiv:0901.3865] [SPIRES].
132. 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].
133. H.M. Sadjadi and M. Jamil, Generalized second law of thermodynamics for FRW cosmology with logarithmic correction, arXiv:1002.3588 [SPIRES].
134. G.W. Gibbons and S.W. Hawking, Cosmological event horizons, thermodynamics and particle creation, Phys. Rev. D 15 (1977) 2738 [SPIRES].
135. T. Jacobson, Thermodynamics of space-time: the Einstein equation of state, Phys. Rev. Lett. 75 (1995) 1260 [gr-qc/9504004] [SPIRES].
136. T. Padmanabhan, Gravity and the thermodynamics of horizons, Phys. Rept. 406 (2005) 49 [gr-qc/0311036] [SPIRES].
137. A.V. Frolov and L. Kofman, Inflation and de Sitter thermodynamics, JCAP 05 (2003) 009 [hep-th/0212327] [SPIRES].
138. U.H. Danielsson, Transplanckian energy production and slow roll inflation Phys. Rev. D 71 (2005) 023516 [hep-th/0411172] [SPIRES].
139. R. Bousso, Cosmology and the S-matrix, Phys. Rev. D 71 (2005) 064024 [hep-th/0412197] [SPIRES].
140. R.-G. Cai and S.P. Kim, First law of thermodynamics and Friedmann equations of Friedmann-Robertson-Walkeruniverse, JHEP 02 (2005) 050 [hep-th/0501055] [SPIRES].
141. M. Akbar and R.-G. Cai, Thermodynamic behavior ofFriedmann equation at apparent horizon of FRWuniverse, Phys. Rev. D 75 (2007) 084003 [hep-th/0609128] [SPIRES].
142. M.R. Setare, Interacting holographic dark energy model and generalized second law of thermodynamics in non-flat universe, JCAP 01 (2007) 023 [hep-th/0701242] [SPIRES].
143. G. Izquierdo and D. Pavon, Dark energy and the generalized second law, Phys. Lett. B 633 (2006) 420 [astro-ph/0505601] [SPIRES].
144. S.A. Fulling, Nonuniqueness of canonical field quantization in Riemannian space-time, Phys. Rev. D 7 (1973) 2850 [SPIRES].
145. P.C.W. Davies, Scalar production in Schwarzschild and Rindler metrics, J. Phys. A 8 (1975) 609 [SPIRES].
146. D. Lohia, Trace anomalies in a two-dimensional de Sitter metric and black body radiation J. Phy. A 11 (1978) 1335 [SPIRES].
147. W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [SPIRES];
148. L.C.B. Crispino, A. Higuchi and G.E.A. Matsas, The Unruh effect and its applications, Rev. Mod. Phys. 80 (2008) 787 [arXiv:0710.5373] [SPIRES].
149. N.D. Birrel and P.C.W. Davies, Quantum Field Theory in curved space-time, Cambridge University Press, Cambridge U.K. (1982).
150. V. Mukhanov and S. Winitzki, Introduction to quantum effects in gravity, Cambridge University Press, Cambridge U.K. (2007).
151. B.S. DeWitt, Quantum Field Theory in curved space-time, Phys. Rept. 19 (1975) 295 [SPIRES].
152. S. Takagi, Vacuum noise and stress induced by uniform accelerator: Hawking-Unruh effect in Rindler manifold ofarbitrary dimensions, Prog. Theor. Phys. Suppl. 88 (1986) 1 [SPIRES].
153. L. Sriramkumar and T. Padmanabhan, Probes of the vacuum structure of quantum fields in classical backgrounds, Int. J. Mod. Phys. D 11 (2002) 1 [gr-qc/9903054] [SPIRES].
154. R. Brout, S. Massar, R. Parentani and P. Spindel, A primer for black hole quantum physics, Phys. Rept. 260 (1995) 329 [arXiv:0710.4345] [SPIRES].
155. R.M. Wald, The thermodynamics ofblack holes, Living Rev. Rel. 4 (2001) 6 [gr-qc/9912119] [SPIRES].
156. J.D. Bekenstein, Non-Archimedean character of quantum buoyancy and the generalized second law ofthermodynamics, Phys. Rev. D 60 (1999) 124010 [gr-qc/9906058] [SPIRES].
157. H. Mohseni Sadjadi, Generalized second law in phantom dominated universe, Phys. Rev. D 73 (2006) 063525 [gr-qc/0512140] [SPIRES].
158. R. Horvat, Holographic dark energy: quantum correlations against thermodynamical description, Phys. Lett. B 664 (2008) 201 [arXiv:0711.4013] [SPIRES].
159. W. Israel, Thermo field dynamics of black holes, Phys. Lett. A 57 (1976) 107 [SPIRES].
160. C. Rovelli, Black hole entropyfrom loop quantum gravity, Phys. Rev. Lett. 77 (1996) 3288 [gr-qc/9603063] [SPIRES].
161. A. Ashtekar, J. Baez, A. Corichi and K. Krasnov, Quantum geometry and black hole entropy, Phys. Rev. Lett. 80 (1998) 904 [gr-qc/9710007] [SPIRES].
162. R.K. Kaul and P. Majumdar, Logarithmic correction to the Bekenstein-Hawking entropy, Phys. Rev. Lett. 84 (2000) 5255 [gr-qc/0002040] [SPIRES].
163. A. Ghosh and P. Mitra, A bound on the log correction to the black hole area law, Phys. Rev. D 71 (2005) 027502 [gr-qc/0401070] [SPIRES].
164. M. Domagala and J. Lewandowski, Black hole entropy from quantum geometry, Class. Quant. Grav. 21 (2004) 5233 [gr-qc/0407051] [SPIRES].
165. K.A. Meissner, Black hole entropy in loop quantum gravity, Class. Quant. Grav. 21 (2004) 5245 [gr-qc/0407052] [SPIRES].
166. S. Hod, High-order corrections to the entropy and area ofquantum black holes, hep-th/0405235 [SPIRES].
167. A.J.M. Medved, A comment on black hole entropy or why nature abhors a logarithm, Class. Quant. Grav. 22 (2005) 133 [gr-qc/0406044] [SPIRES].
168. S.N. Solodukhin, Entropy of Schwarzschild black hole and string-black hole correspondence, Phys. Rev. D 57 (1998) 2410 [hep-th/9701106] [SPIRES].
169. p, Phys. Lett. B 413 (1997) 267 [gr-qc/9707009] [SPIRES].
170. S. Das, P. Majumdar and R.K. Bhaduri, General logarithmic corrections to black hole entropy, Class. Quant. Grav. 19 (2002) 2355 [hep-th/0111001] [SPIRES].
171. G. Gour and A.J.M. Medved, Thermalfluctuations and black hole entropy, Class. Quant. Grav. 20 (2003) 3307 [gr-qc/0305018] [SPIRES].
172. S. Mukherji and S.S. Pal, Logarithmic corrections to black hole entropy and AdS/CFT correspondence, JHEP 05 (2002) 026 [hep-th/0205164] [SPIRES].
173. A. Chatterjee and P. Majumdar, Universal canonical black hole entropy, Phys. Rev. Lett. 92 (2004) 141301 [gr-qc/0309026] [SPIRES].
174. 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].
175. B.R. Majhi, Fermion tunneling beyond semiclassical approximation, Phys. Rev. D 79 (2009) 044005 [arXiv:0809.1508] [SPIRES].