Energy conditions in mimetic-$f(R)$ gravity

TL;DR

This paper investigates the energy conditions in mimetic-$f(R)$ gravity, identifying parameter spaces that allow self-acceleration while satisfying key energy conditions and avoiding instabilities.

Contribution

It characterizes the parameter space of mimetic-$f(R)$ gravity, showing it is larger than that of standard $f(R)$ gravity, and considers stability conditions.

Findings

Parameter space allows self-acceleration with certain energy condition violations.

The parameter space of mimetic-$f(R)$ is larger than standard $f(R)$ gravity.

Stability conditions exclude some regions of the parameter space.

Abstract

The energy conditions of mimetic-$f(R)$ gravity theory is analyzed. We will obtain the parameter space of the theory in some special forms of $f(R)$ in which the self-acceleration is allowed. In this sense, the parameter space is obtained in a way that it violates the strong energy condition while satisfying the weak, null and dominant energy conditions. We will also consider the condition that the Dolgov-Kawasaki instability is avoided. This condition will be further imposed in the parameter space of the theory. We will show that the parameter space of the mimetic-$f(R)$ gravity is larger than $f(R)$ gravity theory.