Stable and Unstable Circular Strings in Inflationary Universes

TL;DR

This paper develops a formalism to analyze fluctuations of circular cosmic strings in various expanding universes, revealing conditions under which inflation stabilizes these strings by damping their fluctuations.

Contribution

It generalizes previous stability results for strings in de Sitter space to arbitrary FRW spacetimes and identifies inflationary regimes that suppress string fluctuations.

Findings

Fluctuations grow slower than the string radius in certain power law inflation cases.

Inflation tends to stabilize circular strings by damping fluctuations.

Stability depends on the specific expansion dynamics of the universe.

Abstract

It was shown by Garriga and Vilenkin that the circular shape of nucleated cosmic strings, of zero loop-energy in de Sitter space, is stable in the sense that the ratio of the mean fluctuation amplitude to the loop radius is constant. This result can be generalized to all expanding strings (of non-zero loop-energy) in de Sitter space. In other curved spacetimes the situation, however, may be different. In this paper we develop a general formalism treating fluctuations around circular strings embedded in arbitrary spatially flat FRW spacetimes. As examples we consider Minkowski space, de Sitter space and power law expanding universes. In the special case of power law inflation we find that in certain cases the fluctuations grow much slower that the radius of the underlying unperturbed circular string. The inflation of the universe thus tends to wash out the fluctuations and to stabilize these strings.