First-order formalism and thick branes in mimetic gravity

TL;DR

This paper develops a first-order formalism for thick branes in mimetic gravity, deriving analytical solutions and analyzing stability and localization of perturbations, which supports recovering four-dimensional gravity.

Contribution

It introduces a novel first-order formalism using super-potentials in mimetic gravity to find analytical thick brane solutions and analyze their stability.

Findings

Both tensor and scalar perturbations are stable.

Tensor zero mode is localized on the brane.

Scalar zero mode is not localized, allowing recovery of 4D gravity.

Abstract

In this paper, we investigate thick branes generated by a scalar field in mimetic gravity theory. By introducing two auxiliary super-potentials, we transform the second-order field equations of the system into a set of first-order equations. With this first-order formalism, several types of analytical thick brane solutions are obtained. Then, tensor and scalar perturbations are analysed. We find that both kinds of perturbations are stable. The effective potentials for the tensor and scalar perturbations are dual to each other. The tensor zero mode can be localized on the brane while the scalar zero mode cannot. Thus, the four-dimensional Newtonian potential can be recovered on the brane.