Cosmology with Branes Wrapping Curved Internal Manifolds

TL;DR

This paper derives solutions for branes wrapping curved manifolds and explores their cosmological implications, showing early internal shrinking and late-time effects due to curvature, extending previous flat manifold models.

Contribution

It introduces new solutions for branes on curved manifolds and analyzes their impact on cosmological evolution, highlighting differences from flat internal spaces.

Findings

Internal dimensions shrink at early times

Unwrapped dimensions expand during early evolution

Curvature effects become significant at late times

Abstract

In this paper we first derive solutions which can be interpreted as branes wrapping nontrivial curved manifolds, and then study their cosmological implications. We find that at early times the branes tend to shrink the internal manifold, while allowing the ``unwrapped'' dimensions to expand in congruence with what has already been observed in the case when the internal manifold is flat (tori). However, at late times the internal curvature terms become important leading to potentially interesting differences.