A critical analysis of modulus stabilization in a higher dimensional F(R) gravity

TL;DR

This paper derives an exact 5D bulk solution in F(R) gravity with de-Sitter branes, analyzes modulus stability across epochs, and demonstrates a stable radion resolving hierarchy issues and enabling a non-singular bounce.

Contribution

It provides a novel exact bulk solution in F(R) gravity with positive powers of R and critically analyzes radion stability in different epochs, linking it to hierarchy resolution.

Findings

Derived exact bulk metric solution for F(R) gravity with de-Sitter branes.

Identified stable radion configurations that address hierarchy problem.

Showed radion exhibits phantom epoch enabling non-singular bounce.

Abstract

An exact solution for the bulk 5-dimensional geometry is derived for F(R) gravity with non-flat de-Sitter 3-branes located at the $M_4 \times Z_2$ orbifold boundaries. The corresponding form of F(R) that leads to such an exact solution of the bulk metric is derived which turns out to have all positive integer powers of R.In such a scenario the stability issue of the modulus (radion field) is analyzed critically for different curvature epochs in both Einstein and Jordan frames. The radion in the effective 4-d theory exhibits a phantom epoch making this model viable for a non-singular bounce. Simultaneous resolution of the gauge hierarchy problem is exhibited through the resulting stable vaue of the radion field in the effective $3+1$ dimensional theory.