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 Lambda CDM model (f = R - Lambda) is quantified by the function m = Rf, (RR)/f,(R). The matter epoch corresponds to m (r = -1) similar or equal to +0 (where r = -Rf, (R)/f) while the accelerated attractor exists in the region 0 <= m <= 1. We find that the equation of state omega(DE) of all such viable f (R) models exhibits two features: omega(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 Supemova 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) greater than or similar to 1, i.e., within reach of observations. If we add local gravity constraints, the bound on in becomes very stringent, with in 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. (C) 2008 Elsevier B.V. All rights reserved.