TY - JOUR

T1 - Phantom crossing, equation-of-state singularities, and local gravity constraints in f (R) models

AU - Amendola, Luca

AU - Tsujikawa, Shinji

N1 - Funding Information:
We thank R. Gannouji, W. Hu, B. Li, D. Polarski and A. Starobinsky for useful discussions. S.T. is supported by JSPS (Grant No. 30318802).

PY - 2008/2/21

Y1 - 2008/2/21

N2 - We identify the class of f (R) dark energy models which have a viable cosmology, i.e. a matter dominated epoch followed by a late-time acceleration. The deviation from a ΛCDM model (f = R - Λ) is quantified by the function m = R f, R R / f, R. The matter epoch corresponds to m (r = - 1) ≃ + 0 (where r = - R f, R / f) while the accelerated attractor exists in the region 0 ≤ m < 1. We find that the equation of state wDE of all such "viable" f (R) models exhibits two features: wDE diverges at some redshift zc and crosses the cosmological constant boundary ("phantom crossing") at a redshift zb smaller than zc. Using the observational data of Supernova Ia and Cosmic Microwave Background, we obtain the constraint m < O (0.1) and we find that the phantom crossing could occur at zb ≳ 1, i.e., within reach of observations. If we add local gravity constraints, the bound on m becomes very stringent, with m several orders of magnitude smaller than unity in the region whose density is much larger than the present cosmological density. The representative models that satisfy both cosmological and local gravity constraints take the asymptotic form m (r) = C (- r - 1)p with p > 1 as r approaches -1.

AB - We identify the class of f (R) dark energy models which have a viable cosmology, i.e. a matter dominated epoch followed by a late-time acceleration. The deviation from a ΛCDM model (f = R - Λ) is quantified by the function m = R f, R R / f, R. The matter epoch corresponds to m (r = - 1) ≃ + 0 (where r = - R f, R / f) while the accelerated attractor exists in the region 0 ≤ m < 1. We find that the equation of state wDE of all such "viable" f (R) models exhibits two features: wDE diverges at some redshift zc and crosses the cosmological constant boundary ("phantom crossing") at a redshift zb smaller than zc. Using the observational data of Supernova Ia and Cosmic Microwave Background, we obtain the constraint m < O (0.1) and we find that the phantom crossing could occur at zb ≳ 1, i.e., within reach of observations. If we add local gravity constraints, the bound on m becomes very stringent, with m several orders of magnitude smaller than unity in the region whose density is much larger than the present cosmological density. The representative models that satisfy both cosmological and local gravity constraints take the asymptotic form m (r) = C (- r - 1)p with p > 1 as r approaches -1.

UR - http://www.scopus.com/inward/record.url?scp=38749143271&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38749143271&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2007.12.041

DO - 10.1016/j.physletb.2007.12.041

M3 - Article

AN - SCOPUS:38749143271

VL - 660

SP - 125

EP - 132

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 3

ER -