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

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Crossing of the phantom divide >・ Various observational data (SN, Cosmic microwavebackground radiation (CMB), BAO) imply that the EoS ofdark energy w DE may evolve from larger than -1 (nonphantomphase) to less than -1 (phantom phase). Namely, itcrosses -1 (the crossing of the phantom divide).w DEà 1z c0zz cRedshift:z ñ 1 aà 1: Red shift at the crossingof the phantom divideNo. 14[Alam, Sahni and Starobinsky, JCAP 0406, 008 (2004)][Nesseris and Perivolaropoulos, JCAP 0701, 018 (2007)][Alam, Sahni and Starobinsky, JCAP 0702, 011 (2007)](a)w DE > à 1Non-phantom phase(b) w DE = à 1Crossing of the phantom divide(c) w DE < à 1Phantom phase
Data fitting of w(z) >zw(z)=w 0 + w 1 1+zNo. 15From [Nesseris and L. Perivolaropoulos, JCAP 0701, 018 (2007)].SN gold data set[Riess et al. [Supernova SearchTeam Collaboration],Astrophys. J. 607, 665 (2004)]SNLS data set[Astier et al. [The SNLSCollaboration], Astron.Astrophys. 447, 31 (2006)]Shaded regionshows 1û error.+Cosmic microwave background radiation (CMB) data[Spergel et al. [WMAP Collaboration], Astrophys. J. Suppl. 170, 3<strong>77</strong> (2007)]SDSS baryon acoustic peak (BAO) data[Eisenstein et al. [SDSS Collaboration], Astrophys. J. 633, 560 (2005)]
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: Models of f(R) gravity (examples) >
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 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
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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
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Other models >No. A-10・Appleby-Ba
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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
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Second law of thermodynamics >[KB a
Page 110 and 111:
Residuals for the best fit to a fla
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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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