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

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.

Accepted in "International Journal of Geometric Methods in Modern Physics",22 pages,no figure

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