Cosmological viable Mimetic $f(R)$ and $f(R,T)$ theories via Noether symmetry

TL;DR

This paper explores Noether symmetries in extended $f(R)$ gravity theories, including $f(R,T)$ and mimetic $f(R)$ models, demonstrating the existence of symmetric classes, stability of solutions, and the possibility of bouncing and $ ext{Lambda}$CDM cosmologies.

Contribution

It identifies classes of $f(R,T)$ and mimetic $f(R)$ models with Noether symmetry and analyzes their stability and cosmological solutions, including bouncing and $ ext{Lambda}$CDM scenarios.

Findings

Existence of Noether symmetric models in extended $f(R)$ theories.

Bouncing and $ ext{Lambda}$CDM solutions are possible in mimetic $f(R)$ gravity.

Some models exhibit future singularities.

Abstract

Extended $f(R)$ theories of gravity have been investigated from the symmetry point of view. We briefly has been investigated Noether symmetry of two types of extended $f(R)$ theories: $f(R,T)$ theory, in which curvature is coupled non minimally to the trace of energy momentum tensor $T_{\mu\nu}$ and mimetic $f (R) $ gravity, a theory with a scalar field degree of freedom, but ghost-free and with internal conformal symmetry. In both cases we write point -like Lagrangian for flat Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological background in the presence of ordinary matter. We have been shown that some classes of models existed with Noether symmetry in these viable extensions of $f(R)$ gravity. As a motivated idea, we have been investigating the stability of the solutions and the bouncing and $\Lambda$CDM models using the Noether symmetries. We have been shown that in mimetic $f(R)$ gravity bouncing and $\Lambda$CDM solutions are possible. Also a class of solutions with future singularities has been investigated.