Tsujikawa, Phys. Rev. D 77, 023507 (2008)

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Bekenstein-Hawking entropy on the apparent horizon inthe flat FLRW background >S = 4GA: Bekenstein-Hawking entropyNo. 30・rà=1/H:: Area of the apparent horizonRadius of the apparent horizon inthe flat FLRW space-timeIt has been shown that it is possible to obtain a picture ofequilibrium thermodynamics on the apparent horizon inthe FLRW background for f(R) gravity due to a suitableredefinition of an energy momentum tensor of the “dark”component that respects a local energy conservation.[KB, Geng and <strong>Tsujikawa</strong>, <strong>Phys</strong>. Lett. B 688, 101 (2010)]In this picture, the horizonà áentropy is simplyexpressed as S = ù/ GH 2 .
Future evolutions of S as functions of z >No. 36Exponential gravity modelñS(z=à1)S0Oscillating behavior:Present value of thehorizon entropy
Page 1:
Equation of state for dark energyin
Page 4 and 5:
(1) General relativistic approach
Page 6 and 7:
m à:mMMDistanceestimator::Apparent
Page 9 and 10:
Canonical scalar field >⎧S þ =
Page 11 and 12:
・In the flat FLRW background, gra
Page 13 and 14:
Models of f(R) gravity (examples) >
Page 15 and 16:
Data fitting of w(z) >zw(z)=w 0 + w
Page 17 and 18:
w DEw DE = à 1< Cosmological evolu
Page 19 and 20:
II. Future crossing of the phantom
Page 21 and 22:
Future evolutions of 1+w DE as func
Page 23 and 24:
III. Equation of state for dark ene
Page 25 and 26:
Combined f(T) theory >No. 25u(> 0):
Page 27 and 28:
A. Non-local gravity< Action >g =de
Page 29 and 30:
・In the flat FLRW space-time, we
Page 31 and 32: ・The finite-time future singulari
Page 33 and 34: ・We estimate the present valueof
Page 35 and 36: Future evolutions of H as functions
Page 37 and 38: ・・In the future ( ), the crossi
Page 39 and 40: Conditions for the viability of f(R
Page 41 and 42: We solve Equations (1) and (2) by i
Page 43 and 44: Equation of state for (the componen
Page 45 and 46: No. 32We consider only non-relativi
Page 47 and 48: Gravitational field equations in th
Page 49: ・By using and ,No. 39・We take a
Page 52 and 53: Future crossing of the phantom divi
Page 54 and 55: B. Relations between the model para
Page 56 and 57: IV. Effective equation of state for
Page 58 and 59: (2) Extension of gravitational theo
Page 60 and 61: Conditions for the viability of f(R
Page 62 and 63: (5) Existence of a matter-dominated
Page 64 and 65: Conclusions of Sec. II >・We have
Page 66 and 67: Conclusions of Sec. IV >No. 64・
Page 68 and 69: ・We assume the flat FLRW space-ti
Page 70 and 71: No. 45p =0.001p =0.01p = à 0.1p =0
Page 72 and 73: (b). Logarithmic f(T) theory >No. 4
Page 74 and 75: The best-fit values >No. 42The mini
Page 76 and 77: (4) Solar system constraintsf(R) gr
Page 78 and 79: (4) Stability of the late-time de S
Page 80 and 81: Data fitting of w(z) (3) >No. B-7Fr
Page 84 and 85: Hu-Sawicki modelStarobinsky’s mod
Page 86 and 87: (a). Exponential f(T) theory >No. 1
Page 88 and 89: (c). Combined f(T) theory >No. 16
Page 90 and 91: p : Constantú Mand P M : Energy de
Page 92 and 93: IV. Effective equation of state for
Page 94 and 95: ・It is known that the finite-time
Page 96 and 97: Other models >No. A-10・Appleby-Ba
Page 98 and 99: w effNo. A-13< Cosmological evoluti
Page 100 and 101: Cosmological evolutions of , and in
Page 102 and 103: Initial conditions >Models of (i),
Page 104 and 105: No. A-21・・ By examining the cos
Page 106 and 107: No. A-23
Page 108 and 109: Second law of thermodynamics >[KB a
Page 110 and 111: Residuals for the best fit to a fla
Page 112 and 113: 5-year WMAP data on >・ For the fl
Page 114 and 115: Appendix B
Page 116 and 117: Recent work >No. B-3[Martinelli, Me
Page 118: (5) Existence of a matter-dominated
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Tsujikawa, Phys. Rev. D 77, 023507 (2008)

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