On String Tunneling in Power Law Inflationary Universes

TL;DR

This paper analyzes the evolution of circular string loops in power law expanding universes, discovering a critical expansion rate that determines whether strings collapse or can tunnel and expand, indicating string nucleation phenomena.

Contribution

It identifies a critical power in power law universes that distinguishes different string evolution behaviors and reveals tunneling solutions indicating string nucleation.

Findings

Existence of a critical power p_m=3+2√2 separating different string behaviors.

Strings can tunnel and expand in universes with p>p_m.

New solutions include contracting from a positive radius to a minimum and then expanding forever.

Abstract

We consider the evolution of circular string loops in power law expanding universes represented by a spatially flat Friedman-Robertson-Walker metric with scale factor $a(t)\propto t^p$ where $t$ is the cosmic time and $p\geq 0$. Our main result is the existence of a "magic" power $p_m=3+2\sqrt{2}$. In spacetimes with $p<p_m$ a circular string expands either forever or to a maximal radius and then contracts until it collapses into a point (black hole). For $p>p_m$, however, we find additional types of solutions. They include configurations which contract from a positive initial radius to a minimal one and then expand forever. Their existence we interpret as an indication for the presence of a finite potential barrier. Equivalently the new solutions signal string nucleation and tunneling, phenomena recently shown to occur in de Sitter space.