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

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V. Summary・ We have discussed modified gravitational theories inorder to explain the current accelerated expansion ofthe universe, so-called dark energy problem.・ We have investigated the equation of state for dark energyin f(R) gravity as well as f(T) theory.w DEw DE = à 1The future crossings of the phantom divide lineare the generic feature in the existingviable f(R) gravity models.No. 34・The crossing of the phantom divide line can berealized in the combined f(T) theory.We have studied the effective equation of state for theuniverse when the finite-time future singularities occurin non-local gravity.
Future evolutions of H as functions of z >No. 23Exponential gravity modelOscillatory behavior:ñH(z=à1)H0‘f’ denotes the valueat the final stagez = à 1.:Present value of theHubble parameter
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: ・We estimate the present valueof
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 82 and 83: Bekenstein-Hawking entropy on the a
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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