Vortices in De Sitter Spacetimes

TL;DR

This paper studies vortex solutions in four-dimensional de Sitter spacetime, revealing static and dynamic configurations that influence spacetime geometry and support a dS/CFT correspondence through a renormalization group interpretation.

Contribution

It extends Nielsen-Olesen vortices to de Sitter space, including dynamic solutions and their implications for spacetime structure and holography.

Findings

Static vortex solutions in de Sitter space

Time-dependent vortex solutions with deficit angles

Evidence for a dS/CFT correspondence via RG flow

Abstract

We investigate vortex solutions to the Abelian Higgs field equations in a four dimensional de Sitter spacetime background. We obtain both static and dynamic solutions with axial symmetry that are generalizations of the Nielsen-Olesen gauge vortices in flat spacetime. The static solution is located in the static patch of de Sitter space. We numerically solve the field equations in an inflationary (big bang) patch and find a time dependent vortex soution, whose effect to create a deficit angle in the spacetime. We show that this solution can be interpreted in terms of a renormalization group flow in accord with a generalized {$c$}-theorem, providing evidence in favour of a dS/CFT correspondence.