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 Tμν 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 ΛCDM models using the Noether symmetries. We have been shown that in mimetic f(R) gravity bouncing and ΛCDM solutions are possible. Also a class of solutions with future singularities has been investigated.

Thick branes with inner structure in mimetic gravity

“…[9] a MOND-like acceleration law was recovered in mimetic gravity in which the mimetic scalar field and matter are non-minimally coupled, and opened up the possibility of addressing the dark matter problem on both galactic and cluster scales. Furthermore, it is possible to unify the late-time acceleration and inflation within this framework [10][11][12][13]. To obtain a viable theory confronted with the cosmic evolution, this theory is transformed to Lagrange multiplier formulation and the potential of the mimetic scalar field is considered.…”

“…For more recent work concerning mimetic gravity see Refs. [5][6][7][8][11][12][13][17][18][19][20][21][22][23][24][25][26] or Ref.…”

Spherically symmetric static vacuum solutions in Mimetic gravity

“…[4] mimetic gravity has been analyzed in the framework of F (R)-modified gravity and in Refs. [5,6] the energy conditions for this kind of models have been investigated. In Ref.…”

Cosmological analysis of scalar field models in f(R, T) gravity

“…Hussain et al [19] investigated the existence of Noether symmetry of a power-law f (R) model and found the boundary term to vanish for the flat FRW universe model but Shamir et al [20] obtained a non-zero boundary term of the same model. Momeni et al [21] explored a Noether point symmetry of the isotropic universe in mimetic f (R) and f (R, T ) gravity theories. Shamir and Ahmad [22] constructed exact solutions in f (G, T ) gravity (G denotes the Gauss-Bonnet term).…”