Scaling solution for small cosmic string loops

TL;DR

This paper presents a solution to the evolution of small cosmic string loops considering gravitational radiation, demonstrating a stable scaling regime where the energy density remains finite over time.

Contribution

It introduces an analytical solution for the loop number density evolution including gravitational radiation effects, highlighting the conditions for a finite energy density in the scaling regime.

Findings

The solution converges to a scaling regime with finite energy density.

Gravitational radiation causes loops to shrink and decay over time.

The model applies to both infrared and ultraviolet regimes.

Abstract

The equation governing the time evolution of the number density of loops in a cosmic string network is a detailed balance determined by energy conservation. We solve this equation with the inclusion of the gravitational radiation effect which causes the loops to shrink (and eventually decay) as time elapses. The solution approaches a scaling regime in which the total energy density in loops remains finite, converging both in the infrared and in the ultraviolet.