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

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=Rf,RR/f,R. The matter epoch corresponds to m(r=−1)≃+0 (where r=−Rf,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 m1 as r approaches −1.