Tsujikawa, Phys. Rev. D 77, 023507 (2008)
Tsujikawa, Phys. Rev. D 77, 023507 (2008) Tsujikawa, Phys. Rev. D 77, 023507 (2008)
B. Relations between the model parameters and the propertyof the finite-time future singularities・f s and û characterize the theory ofnon-local gravity.h s , t q・s and specify the property ofthe finite-time future singularity.・・ñ cø cand determine a leading-order solution in terms offor the gravitational field equations in the flat FLRW space-time.When ,for ,for and ,for ,H ú effú sfor , asymptotically becomes finite and alsoasymptotically approaches a finite constant value .for , →∞,,No. 17
B. Estimation of the current value of the effective equation of No. 22state parameter for non-local gravity [Komatsu et al. [WMAP Collaboration],・・The limit on a constant equation ofstate for dark energy in a flatuniverse has been estimated asFor a time-dependent equation of statefor dark energy, by using a linear form,constraints on andhave been found as,Astrophys. J. Suppl. 192, 18 (2011)]by combining the data of Seven-Year Wilkinson MicrowaveAnisotropy Probe (WMAP)Observations with the latestdistance measurements from thebaryon acoustic oscillations(BAO) in the distribution ofgalaxies and the Hubble constantmeasurement.: Current value of: Derivative ofw DEw DEfrom the combination of theWMAP data with the BAO data,the Hubble constant measurementand the high-redshift SNe Ia data.
- 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 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),
B. Estimation of the current value of the effective equation of No. 22state parameter for non-local gravity [Komatsu et al. [WMAP Collaboration],・・The limit on a constant equation ofstate for dark energy in a flatuniverse has been estimated asFor a time-dependent equation of statefor dark energy, by using a linear form,constraints on andhave been found as,Astrophys. J. Suppl. 192, 18 (2011)]by combining the data of Seven-Year Wilkinson MicrowaveAnisotropy Probe (WMAP)Observations with the latestdistance measurements from thebaryon acoustic oscillations(BAO) in the distribution ofgalaxies and the Hubble constantmeasurement.: Current value of: Derivative ofw DEw DEfrom the combination of theWMAP data with the BAO data,the Hubble constant measurementand the high-redshift SNe Ia data.
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