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

TL;DR

The paper develops a general reconstruction framework for $f(R)$ gravity from any realistic FRW cosmology using an auxiliary field, yielding an implicit $f(R)$ of the form $f(R)=P(\phi(R))R+Q(\phi(R))$ and a master equation for $P(\phi)$ that encodes the cosmic history. It delivers explicit, exactly solvable examples, including a ΛCDM-type cosmology without an explicit cosmological constant and models that smoothly transition from matter domination to late-time acceleration, while showing stability and a negligible Newtonian correction under appropriate conditions. It also discusses a compensating dark energy approach that augments $f(R)$ to realize matter-era dynamics, with the late-time acceleration arising from the curvature terms. The results demonstrate that realistic cosmologies can be realized in modified gravity theories that remain compatible with Solar System tests, offering a viable alternative framework to explain dark energy and guiding future observational tests and perturbation analyses.

Abstract

We develop the general scheme for modified $f(R)$ gravity reconstruction from any realistic 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 decceleration to acceleration, accelerating epoch consistent with recent WMAP data b. $Λ$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 curvature). In the alternative approach, it is demonstrated that even simple versions of modified gravity may lead to the unification of matter dominated and accelerated phases at the price of the introduction of compensating dark energy.