Fundamental energy scale of the thick brane in mimetic gravity

TL;DR

This paper explores thick brane solutions in mimetic gravity, analyzing their stability, gravitational localization, and corrections to Newtonian gravity, leading to constraints on fundamental energy scales from experimental data.

Contribution

It provides three new stable thick brane solutions in mimetic gravity with detailed analysis of gravitational localization and experimental constraints on energy scales.

Findings

All solutions are stable under tensor perturbations.

Zero modes of gravitons are localized on the brane.

Experimental data constrains the fundamental scale to be above 10^5 TeV.

Abstract

In this paper, thick branes generated by the mimetic scalar field with Lagrange multiplier formulation are investigated. We give three typical thick brane background solutions with different asymptotic behaviors and show that all the solutions are stable under tensor perturbations. The effective potentials of the tensor perturbations exhibit as volcano potential, Po\"{o}schl-Teller potential, and harmonic oscillator potential for the three background solutions, respectively. All the tensor zero modes (massless gravitons) of the three cases can be localized on the brane. We also calculate the corrections to the Newtonian potential. On a large scale, the corrections to the Newtonian potential can be ignored. While on a small scale, the correction from the volcano-like potential is more pronounced than the other two cases. Combining the specific corrections to the Newtonian potential of these three cases and the latest results of short-range gravity experiments, we get the constraint on the scale parameter as $k\gtrsim 10^{-4}$eV, and constraint on the corresponding five-dimensional fundamental scale as $M_\ast \gtrsim10^5$TeV.