Modified f ( R ) gravity consistent with realistic cosmology: From a matter dominated epoch to a dark energy universe

We develop the general scheme for modified $f(R)$ gravity reconstruction from any realistic Friedmann-Robertson-Walker (FRW) cosmology. We formulate several versions of modified gravity compatible with solar system tests where the following sequence of cosmological epochs occurs: (a) matter dominated phase (with or without usual matter), transition from deceleration to acceleration, accelerating epoch consistent with recent WMAP data, (b) $\ensuremath{\Lambda}\mathrm{CDM}$ cosmology without cosmological constant. As a rule, such modified gravities are expressed implicitly (in terms of special functions) with late-time asymptotics of known type (for instance, the model with negative and positive powers of…