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

Abstract

Abstract 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 w DE of all such “viable” f ( R ) models exhibits two features: w DE diverges at some redshift z c and crosses the cosmological constant boundary (“phantom crossing”) at a redshift z b smaller than z c . 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 z b ≳ 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.