The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration

TL;DR

This paper investigates the future evolution of the universe in $F(R)$-gravity models that unify inflation and late-time acceleration, analyzing potential singularities and how quantum effects can prevent them.

Contribution

It demonstrates that certain $F(R)$-gravity models can classically develop various future singularities, but quantum effects may prevent their occurrence, and proposes models free of future singularities.

Findings

Classical models can develop Big Rip and other singularities.

Quantum effects can prevent the formation of future singularities.

A realistic $F(R)$-gravity model free of future singularities is proposed.

Abstract

We study the future evolution of quintessence/phantom dominated epoch in modified $F(R)$-gravity which unifies the early-time inflation with late-time acceleration and which is consistent with observational tests. Using the reconstruction technique it is demonstrated that there are models where any known (Big Rip, II, III or IV Type) singularity may classically occur. From another side, in Einstein frame (scalar-tensor description) only IV Type singularity occurs. Near the singularity the classical description breaks up, it is demonstrated that quantum effects act against the singularity and may prevent its appearance. The realistic $F(R)$-gravity which is future singularity free is proposed. We point out that additional modification of any $F(R)$-gravity by the terms relevant at the early universe is possible, in such a way that future singularity does not occur even classically.