Sidestepping the Cosmological Constant with Football-Shaped Extra Dimensions

TL;DR

This paper introduces an exact football-shaped two-extra-dimensional brane-world model stabilized by magnetic flux, which remains insensitive to brane vacuum energy, offering a new approach to the cosmological constant problem.

Contribution

It provides an explicit, stable solution with a football-shaped compactification that decouples brane vacuum energy from the four-dimensional cosmological constant.

Findings

The model achieves a flat brane geometry despite brane vacuum energy.

The extra dimensions are stabilized by magnetic flux and a bulk cosmological constant.

The geometry is insensitive to changes in brane vacuum energy, affecting only the conical deficit.

Abstract

We present an exact solution for a factorizable brane-world spacetime with two extra dimensions and explicit brane sources. The compactification manifold has the topology of a two-sphere, and is stabilized by a bulk cosmological constant and magnetic flux. The geometry of the sphere is locally round except for conical singularities at the locations of two antipodal branes, deforming the sphere into an American-style football. The bulk magnetic flux needs to be fine-tuned to obtain flat geometry on the branes. Once this is done, the brane geometry is insensitive to the brane vacuum energy, which only affects the conical deficit angle of the extra dimensions. Solutions of this form provide a new arena in which to explore brane-world phenomenology and the effects of extra dimensions on the cosmological constant problem.