Cosmology in the mimetic higher-curvature $$f(R,R_{\mu \nu }R^{\mu \nu })$$ gravity

Abstract

In the framework of the mimetic approach, we study the $$f(R,R_{\mu \nu }R^{\mu \nu })$$ f ( R , R μ ν R μ ν ) gravity with the Lagrange multiplier constraint and the scalar potential. We introduce field equations for the discussed theory and overview their properties. By using the general reconstruction scheme we obtain the power law cosmology model for the $$f(R,R_{\mu \nu }R^{\mu \nu })=R+d(R_{\mu \nu }R^{\mu \nu })^p$$ f ( R , R μ ν R μ ν ) = R + d ( R μ ν R μ ν ) p case as well as the model that describes symmetric bounce. Moreover, we reconstruct model, unifying both matter dominated and accelerated phases, where ordinary matter is neglected. Using inverted reconstruction scheme we recover specific $$f(R,R_{\mu \nu }R^{\mu \nu })$$ f ( R , R μ ν R μ ν ) function which give rise to the de-Sitter evolution. Finally, by employing the perfect fluid approach, we demonstrate that this model can realize inflation consistent with the bounds coming from the BICEP2/Keck array and the Planck data. We also discuss the holographic dark energy density in terms of the presented $$f(R,R_{\mu \nu }R^{\mu \nu })$$ f ( R , R μ ν R μ ν ) theory. Thus, it is suggested that the introduced extension of the mimetic regime may describe any given cosmological model.

Precession shift in curvature based extended theories of gravity and quintessence fields

“…In the case of Scalar Tensor Fourth Order Gravity, we find that the parameters of the model are given by (see Eqs. (32,31,30)…”

“…It must be mentioned that modifications of GR are also motivated by the fact that Einstein's theory of gravity breaks down in the UV [12,13]. Such deviations from General Relativity occurs in several frameworks, such as Brans-Dicke and scalar-tensor (ST) theories [14][15][16], braneworld theories [17][18][19][20][21][22], higher order invariants such as f (R) and f (φ, R, R 2 , R µν R µν , R) (which correspond to Einstein's gravity plus one or multiple conformally coupled scalar fields [23][24][25][26]) [27][28][29][30][31], noncommutative geometry [32], and compactified extra dimension/Kaluza-Klein models [33][34][35][36][37][38]. Moreover, they can also be generated from higher-order terms in the curvature invariants, nonminimal couplings to the background geometry in the Hilbert-Einstein Lagrangian [39][40][41][42].…”

Isotropic stellar model in mimetic theory

“…It has been shown that for a spherically symmetric spacetime the only solution is the Schwarzschild spacetime which means that the Birkhoff's theorem is hold. Moreover, mimetic theory have been extended to f (R) gravity [54][55][56][57][58][59][60][61][62][63][64][65][66][67] and to Gauss-Bonnet gravitational theory [68][69][70][71][72]. More specifically, a unified scenario of early inflation and late-time acceleration in the framework of mimetic f (R) gravity was formulated in [73].…”

Physical aspects of ${f}(R,G_{μν}T^{μν})$ modified gravity theories

“…In the modified gravity theories, a particular invariant based on the contraction between the matter energy-momentum tensor and the Ricci tensor R µν T µν has been considered [43,61], taking into account a possible interplay between the space-time geometry and the fundamental characteristics of the matter component, embedded into the specific form of the energy-momentum tensor. From a theoretical perspective, such an approach is viable and can lead to different effects [62][63][64][65][66][67][68][69][70][71]. From this, the extension towards an invariant based on the interplay between the Einstein tensor and the energy-momentum tensor occurs naturally [72] and can lead to a viable modified gravity theory.…”