Aspects of Late-time Evolution in Mimetic $F(R)$ Gravity

TL;DR

This paper explores how mimetic $F(R)$ gravity models can unify early and late-time cosmic acceleration, highlighting the advantages of exponential $F(R)$ models and analyzing their impact on cosmic evolution and structure growth.

Contribution

It demonstrates that mimetic $F(R)$ gravity can resolve issues in ordinary models and unifies early and late-time acceleration using exponential $F(R)$ functions.

Findings

Exponential $F(R)$ models effectively unify cosmic acceleration phases.

Mimetic $F(R)$ models remedy pathologies of ordinary $F(R)$ models.

Significant differences in growth factor are observed between mimetic and ordinary models.

Abstract

We demonstrate how to describe in an unified way early and late-time acceleration in the context of mimetic $F(R)$ gravity. As we show, an exponential $F(R)$ gravity model has appealing features, with regard to unification, and we perform an analysis of the late-time evolution. The resulting picture is interesting since in the mimetic case, certain pathologies of some ordinary $F(R)$ models are remedied in a consistent way, owing to the presence of the mimetic potential and the Lagrange multiplier. We quantify the late-time evolution analysis by studying the scaled dark energy density, the dark energy equation of state and the total effective equation of state, and as we show the late-time evolution is crucially affected by the functional form of the $F(R)$ gravity. It is intriguing that the most appealing case corresponds to the exponential $F(R)$ gravity which unifies late and early-time acceleration. Finally, we study the behavior of the effective gravitational constant and the growth factor, and as we show, significant differences between the mimetic and ordinary $F(R)$ exponential model are spotted in the growth factor.