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.