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

Abstract

We consider flat solutions in a brane world model with a massless scalar field appearing in 5D H-MNPQ(2). Since those solutions have naked bulk singularities or are such that the 4D Planck mass is divergent, we should have a compact extra dimension, the size of which is then fixed by brane tension(s) and the bulk cosmological constant. By inspecting scalar perturbations around the flat solutions, we find that there is no zero mode for the radion and radion modes have only positive masses. This result confirms the fact that the radius of the extra dimension cannot be adjusted independently of the parameters of the model, and thus that the model considered does not solve the problems encountered in other approaches to the self-tuning of the cosmological constant.