Tsujikawa, Phys. Rev. D 77, 023507 (2008)
Tsujikawa, Phys. Rev. D 77, 023507 (2008) Tsujikawa, Phys. Rev. D 77, 023507 (2008)
Gravitational field equation >No. 28・ ñ・The variation of the action with respect to gives*0: Energy-momentum tensor of matter(prime) : Derivative with respect toWe assume the flat FLRW space-time with the metric and considerthe case in which the scalar fields ñ and ø only depend on time.Gravitational field equations in the FLRW background:ñ< Equations of motion for ñ and ø >,and :Energy density andpressure of matter.
・In the flat FLRW space-time, we analyze an asymptoticsolution of the gravitational field equations in the limit ofthe time when the finite-time future singularities appear.We consider the case in which the Hubble parameter is expressed ash s : Positive constant,q : Non-zero constant larger than -1When , →∞.t s・No. 29Scale factor :・ We have .ñ c ,a s : Constantø c : Integration constants・We take a form of f(ñ) as .,: Non-zero constants
- 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: A. Non-local gravity< Action >g =de
- 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
・In the flat FLRW space-time, we analyze an asymptoticsolution of the gravitational field equations in the limit ofthe time when the finite-time future singularities appear.We consider the case in which the Hubble parameter is expressed ash s : Positive constant,q : Non-zero constant larger than -1When , →∞.t s・No. 29Scale factor :・ We have .ñ c ,a s : Constantø c : Integration constants・We take a form of f(ñ) as .,: Non-zero constants
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