Singular Inflationary Universe from $F(R)$ Gravity

TL;DR

This paper investigates how Type IV finite-time singularities in $F(R)$ gravity influence cosmic evolution, particularly during inflation, and explores their potential role in triggering graceful exit and unifying early and late-time acceleration.

Contribution

It demonstrates that Type IV singularities affect Hubble flow parameters, can induce dynamical instabilities for graceful exit, and shows how such singularities can be incorporated into inflation models within $F(R)$ gravity.

Findings

Type IV singularities cause singularities in Hubble flow parameters.

Dynamical instabilities at the singularity can trigger graceful exit from inflation.

Models can unify early and late-time cosmic acceleration.

Abstract

Unlike crushing singularities, the so-called Type IV finite-time singularity offers the possibility that the Universe passes smoothly through it, without any catastrophic effects. Then the question is if the effects of a Type IV singularity can be detected in the process of cosmic evolution. In this paper we address this question in the context of $F(R)$ gravity. As we demonstrate, the effects of a Type IV singularity appear in the Hubble flow parameters, which determine the dynamical evolution of the cosmological system. So we study various inflation models incorporating a Type IV singularity, with the singularity occurring at the end of inflation. Particularly we study a toy model and a singular version of the $R^2$ gravity Hubble rate. As we evince, some of the Hubble flow parameters become singular at the singularity, an effect which indicates that at that point a dynamical instability occurs. This dynamical instability eventually indicates the graceful exit from inflation. We demonstrate that the toy model has an unstable de Sitter point at the singularity, so indeed graceful exit could be triggered. In the case of the singular inflation model, graceful exit proceeds in the standard way. In the case of the singular inflation model, we found various scenarios for singular evolution, most of which are compatible with observations, and only one leads to severe instabilities. We also compare the ordinary Starobinsky with the singular inflation model, and we point out the qualitative and quantitative differences. Finally, we study the late-time dynamics of the toy model and of the singular inflation model and we demonstrate that the unification of early and late-time acceleration can be achieved. We also show that it is possible to achieve late-time acceleration similar to the $\Lambda$-Cold Dark Matter model.