Cosmology in the mimetic higher-curvature f(R, Rμν Rμν) gravity

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. We also discuss the holographic dark energy density in terms of the presented f(R, R-mu nu R-mu nu) theory. Thus, it is suggested that the introduced extension of the mimetic regime may describe any given cosmological model.

Automated summary

The study examines the f(R, R-μνR-μν) gravity theory within the mimetic approach, involving field equations, cosmological models, and inflation consistency. Reconstruction schemes are used to derive specific models and discuss dark energy density, indicating the potential of mimetic extension in describing diverse cosmological scenarios.