Cyclic, ekpyrotic and little rip universe in modified gravity

TL;DR

This paper reconstructs specific $F(R)$ gravity models that can produce cyclic, ekpyrotic, and little rip cosmological scenarios, offering alternatives to standard $ ext{Λ}$CDM and analyzing their properties and differences.

Contribution

It introduces new $F(R)$ gravity models capable of realizing cyclic, ekpyrotic, and little rip universes, and compares them with scalar-tensor theories and standard cosmology.

Findings

Explicit $F(R)$ models for cyclic and ekpyrotic universes

An $F(R)$ model for little rip evolution compatible with $ ext{Λ}$CDM

Transformation of little rip solutions leads to Big Bang singularity in Einstein frame

Abstract

We propose the reconstruction of $F(R)$ gravity in such a way that corresponding theory admits cyclic and ekpyrotic universe solutions. The number of explicit examples of such $F(R)$ model is found. The comparison with the reconstructed scalar-tensor theory is made. We also present $F(R)$ gravity which provides the little rip evolution and gives the realistic gravitational alternative for $\Lambda$CDM cosmology. The time for little rip dissolution of bound structures in such theory is estimated. We demonstrate that transformed little rip $F(R)$ solution becomes qualitatively different cosmological solution with Big Bang type singularity in Einstein frame.