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

TL;DR

This paper explores mimetic higher-curvature $f(R,R_{ u ho}R^{ u ho})$ gravity, deriving models that describe various cosmological phases including inflation, bounce, and de-Sitter expansion, using reconstruction techniques.

Contribution

It introduces a novel mimetic $f(R,R_{ u ho}R^{ u ho})$ gravity framework with reconstruction methods to model diverse cosmological scenarios.

Findings

Power law cosmology and bounce models constructed.

Unified matter-dominated and accelerated phases achieved.

Inflation consistent with BICEP2/Keck and Planck data demonstrated.

Abstract

In the framework of the mimetic approach, we study the $f(R,R_{\mu\nu}R^{\mu\nu})$ 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 $f(R,R_{\mu\nu}R^{\mu\nu})=R+d(R_{\mu\nu}R^{\mu\nu})^p$ 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 $f(R,R_{\mu\nu}R^{\mu\nu})$ 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. Thus, it is suggested that the introduced extension of the mimetic regime may describe any given cosmological model.