Wave function of the radion in the brane background with a massless scalar field and a self-tuning problem

TL;DR

This paper analyzes the stability of flat brane solutions with a massless scalar field in 5D, showing that the radion mode is projected out, which challenges the self-tuning approach to the cosmological constant problem.

Contribution

It demonstrates that the massless radion mode is eliminated by boundary conditions, indicating fixed extra dimensions are incompatible with self-tuning in this setup.

Findings

Flat solutions are stable with positive radion mass spectrum.

Radion mode is projected out by boundary conditions.

Fixed extra dimension does not support self-tuning of the cosmological constant.

Abstract

We consider flat solutions in the brane background with a massless scalar field appearing in 5D $H^2_{MNPQ}$. Since there exist bulk singularities or arises the divergent 4D Planck mass, we should introduce a compact extra dimension, the size of which is then fixed by brane tension(s) and a bulk cosmological constant. Inspecting scalar perturbations around the flat solutions, we find that the flat solutions are stable vacua from the positive mass spectrum of radion. We show that the massless radion mode is projected out by the boundary condition arising in cutting off the extra dimension. Thus, the fixed extra dimension is not alterable, which is not useful toward a self-tuning of the cosmological constant.