Anisotropic Extra Dimensions

TL;DR

This paper explores a five-dimensional model with anisotropic extra dimensions, finding maximally symmetric solutions and analyzing scalar perturbations that reveal ghost modes even when symmetry is restored.

Contribution

It introduces a novel anisotropic extra-dimensional setup and examines its background solutions and perturbation spectrum, highlighting persistent ghost modes.

Findings

Maximally symmetric solutions with anisotropic scaling found

Background solutions resemble warped metrics similar to Randall-Sundrum

Ghost scalar modes persist even when diffeomorphism invariance is restored

Abstract

We consider the scenario where in a five-dimensional theory, the extra spatial dimension has different scaling than the other four dimensions. We find background maximally symmetric solutions, when the bulk is filled with a cosmological constant and at the same time it has a three-brane embedded in it. These background solutions are reminiscent of Randall-Sundrum warped metrics, with bulk curvature depending on the parameters of the breaking of diffeomorphism invariance. Subsequently, we consider the scalar perturbation sector of the theory and show that it has certain pathologies and the striking feature that in the limit where the diffeomorphism invariance is restored, there remain ghost scalar mode(s) in the spectrum.