Reconstructing Mimetic Cosmology

TL;DR

This paper reconstructs the potential in mimetic gravity using a parametrization approach, deriving analytical solutions and numerically reconstructing the potential as a function of the scalar field, with implications for cosmology.

Contribution

It introduces a method to reconstruct the scalar potential in mimetic gravity without assuming a specific form, using the CPL parametrization and analytical as well as numerical techniques.

Findings

Derived explicit potential functions in terms of redshift.

Obtained analytical solutions in the mimetic gravity framework.

Performed numerical reconstruction of the potential V(φ).

Abstract

We explore the mimetic gravity formulation with the inclusion of a scalar field potential namely, $V(\phi)$. However, we are not considering any {\it a priori} specific form this term. By means of the Chevallier-Polarski-Linder parametrization for the parameter state of the fluid we can construct an explicit function for such potential in terms of the cosmological redshift and obtain analytical solutions in the mimetic gravity approach. We revise some cosmological implications of these results and additionally we perform a numerical reconstruction for the potential $V$ as a function of the mimetic scalar field, $\phi$.