Numerical Solutions of Inflating Higher Dimensional Global Defects

TL;DR

This paper numerically investigates higher-dimensional global defects, analyzing how the expansion rate relates to symmetry-breaking scale and extra dimensions, with implications for cosmological constant solutions.

Contribution

It provides the first detailed numerical solutions of Einstein and scalar field equations for global defects in six or more dimensions, exploring their cosmological implications.

Findings

Expansion rate $H$ increases with symmetry-breaking scale $ta$.

Expansion rate $H$ decreases as the number of extra dimensions $n$ increases.

Cigar geometry of extra dimensions is not necessary for the observed behavior.

Abstract

We find numerical solutions of Einstein equations and scalar field equation for a global defect in higher dimensional spacetimes ($\geq 6$). We examine in detail the relation among the expansion rate $H$ and the symmetry-breaking scale $\eta$ and the number of extra dimensions $n$ for these solutions. We find that even if the extra dimensions do not have a cigar geometry, the expansion rate $H$ grows as $\eta$ increases, which is opposite to what is needed for the recently proposed mechanism for solving the cosmological constant problem. We also find that the expansion rate $H$ decreases as $n$ increases.