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

TL;DR

The paper addresses the possibility of finite-time future singularities in $F(R)$ gravity that unifies early-time inflation with late-time acceleration. It employs a reconstruction technique to realize various cosmologies in the Jordan frame and analyzes the frame mapping to the Einstein frame, where singularities reduce to Type $IV$. It shows that quantum corrections via the conformal anomaly, or the inclusion of an $R^2$-type term, can prevent such singularities, and it presents a concrete, realistic $F(R)$ model that maintains inflation and late-time acceleration while remaining compatible with local tests. The results provide a framework for building singularity-free modified gravity models and highlight the role of early-universe modifications in ensuring long-term cosmological viability and solar-system consistency.

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.