Regularized braneworlds of arbitrary codimension

TL;DR

This paper studies thick p-branes in higher-dimensional spacetimes, deriving conditions for flatness and cosmology, and discusses the challenges of localizing gravity due to infinite transverse volume.

Contribution

It provides a general framework for regularized thick branes of arbitrary codimension and analyzes their cosmological dynamics and gravity localization issues.

Findings

Flat brane solutions require specific fine-tuning between brane and bulk parameters.

Regularization avoids singularities but leads to infinite transverse volume.

Gravity cannot be localized without an infrared cutoff due to infinite transverse dimensions.

Abstract

We consider a thick p-brane embedded in an n-dimensional spacetime possessing radial symmetry in the directions orthogonal to the brane. We first consider a static brane, and find a general fine tuning relationship between the brane and bulk parameters required for the brane to be flat. We then consider the cosmology of a time dependent brane in a static bulk, and find the Friedmann equation for the brane scale factor a(t). The singularities that would ordinarily arise when considering arbitrary codimensions are avoided by regularizing the brane, giving it a finite profile in the transverse dimensions. However, since we consider the brane to be a strictly local defect, we find that the transverse dimensions must have infinite volume, and hence gravity cannot be localized on the brane without resorting to some infra-red cutoff.