Inflating magnetically charged braneworlds

TL;DR

This paper numerically investigates inflating magnetic monopole solutions in higher-dimensional spacetimes, revealing how defect properties change with symmetry-breaking scale and providing exact solutions for inflating monopoles.

Contribution

It introduces new analytic solutions for inflating monopoles in higher dimensions and analyzes the parameter space, extending understanding beyond static defect configurations.

Findings

Critical symmetry-breaking scale determines defect geometry

Inflating solutions have de Sitter worldsheets and cigar-shaped extra dimensions

Exact asymptotic solutions for inflating monopoles are derived

Abstract

Numerical solutions of Einstein, scalar, and gauge field equations are found for static and inflating defects in a higher-dimensional spacetime. The defects have $(3+1)$-dimensional core and magnetic monopole configuration in $n=3$ extra dimensions. For symmetry-breaking scale $\eta$ below the critical value $\eta_c$, the defects are characterized by a flat worldsheet geometry and asymptotically flat extra dimensions. The critical scale $\eta_c$ is comparable to the higher-dimensional Planck scale and has some dependence on the gauge and scalar couplings. For $\eta=\eta_c$, the extra dimensions degenerate into a `cigar', and for $\eta>\eta_c$ all static solutions are singular. The singularity can be removed if the requirement of staticity is relaxed and defect cores are allowed to inflate. The inflating solutions have de Sitter worldsheets and cigar geometry in the extra dimensions. Exact analytic solutions describing the asymptotic behavior of these inflating monopoles are found and the parameter space of these solutions is analyzed.