Gravity in higher codimension de Sitter Brane Worlds

TL;DR

This paper investigates higher codimension de Sitter brane solutions in Einstein's gravity, revealing conditions for graviton localization and the influence of bulk cosmological constant on internal dimensions.

Contribution

It provides new solutions for codimension n>2 defects with de Sitter slices, analyzing graviton equations and boundary conditions for localization.

Findings

Localization occurs only with negative bulk cosmological constant

The internal (n-1)-sphere size depends on defect symmetry breaking scale

Solutions have naked singularities that satisfy no-flow conditions

Abstract

We study solutions of Einstein's equations corresponding codimension n>2 global topological defects with de Sitter slices. We analyze a class of solutions that are cylindrically symmetric and admit positive, negative or zero bulk cosmological constant. We derive the relevant graviton equations. For an extended brane, the properties of the solution depend on apropriate boundary conditions that the exterior solutions have to satisfy near the core. As an alternative we consider matching copies of the exterior solution related by symmetry. We show that we can get localization only when the bulk cosmological constant is negative. We obtain a condition on the global defect symmetry breaking scale which ultimately controls the size of the n-1 internal dimensions at the position of the brane. The induced metric on the brane, in the case of mirror spacetimes, is a direct product of a de Sitter space and an (n-1)-sphere, while the metric of the embedding spacetime is a warped product and the actual size of the (n-1)-sphere changes as we move along the radial direction. The solutions possess naked singularities, which nevertheless satisfy no-flow conditions.