Blown-up p-Branes and the Cosmological Constant

TL;DR

This paper explores a specific brane-world model with extra dimensions, finding a singularity-free solution but concluding that it does not resolve the cosmological constant problem and introduces hierarchy issues.

Contribution

It provides a new singularity-free solution for blown-up p-branes with extra dimensions, analyzing implications for gravity and the cosmological constant problem.

Findings

The solution is singularity-free in the bulk and on the brane.

Fine-tuning is required between the brane's cosmological constant and the extra-dimensional volume.

A large warp factor is needed for 4D gravity, worsening the hierarchy problem.

Abstract

We consider a blown-up 3-brane, with the resulting geometry R^(3,1) \times S^(N-1), in an infinite-volume bulk with N > 2 extra dimensions. The action on the brane includes both an Einstein term and a cosmological constant. Similar setups have been proposed both to reproduce 4-d gravity on the brane, and to solve the cosmological constant problem. Here we obtain a singularity-free solution to Einstein's equations everywhere in the bulk and on the brane, which allows us to address these question explicitely. One finds, however, that the proper volume of S^(N-1) and the cosmological constant on the brane have to be fine-tuned relatively to each other, thus the cosmological constant problem is not solved. Moreover the scalar propagator on the brane behaves 4-dimensionally over a phenomenologically acceptable range only if the warp factor on the brane is huge, which aggravates the Weak Scale - Planck Scale hierarchy problem.