Tsujikawa, Phys. Rev. D 77, 023507 (2008)
Tsujikawa, Phys. Rev. D 77, 023507 (2008) Tsujikawa, Phys. Rev. D 77, 023507 (2008)
IV. Effective equation of state for the universe and thefinite-time future singularities in non-local gravityNo. 26Non-local gravityproduced by quantum effects[Deser and Woodard, Phys. Rev. Lett. 99, 111301 (2007)]・ It is known that so-called matter instability occurs in F(R) gravity.[Dolgov and Kawasaki, Phys. Lett. B 573, 1 (2003)]This implies that the curvature inside matter sphere becomesvery large and hence the curvature singularity could appear.[Arbuzova and Dolgov, Phys. Lett. B 700, 289 (2011)]It is important to examine whether there exists the curvaturesingularity, i.e., “the finite-time future singularities”in non-local gravity.
A. Non-local gravity< Action >g =det(g ö÷ )f : Some function: Metric tensorNo. 27Λ : Cosmological constantNon-local gravityBy introducing two scalar fields and , we find・By the variation of the action in thefirst expression over ø , we obtain(or )Substituting this equation into the action in thefirst expression, one re-obtains the starting action.: Covariant derivative operator: Covariant d'Alembertian: Matter LagrangianQ: Matter fields
- 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: Combined f(T) theory >No. 25u(> 0):
- 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
IV. Effective equation of state for the universe and thefinite-time future singularities in non-local gravityNo. 26Non-local gravityproduced by quantum effects[Deser and Woodard, <strong>Phys</strong>. <strong>Rev</strong>. Lett. 99, 111301 (2007)]・ It is known that so-called matter instability occurs in F(R) gravity.[Dolgov and Kawasaki, <strong>Phys</strong>. Lett. B 573, 1 (2003)]This implies that the curvature inside matter sphere becomesvery large and hence the curvature singularity could appear.[Arbuzova and Dolgov, <strong>Phys</strong>. Lett. B 700, 289 (2011)]It is important to examine whether there exists the curvaturesingularity, i.e., “the finite-time future singularities”in non-local gravity.
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