Non-linear dynamics of cosmic strings with non-scaling loops

TL;DR

This paper introduces a simple analytical model for cosmic string networks with non-scaling loops, predicting new length scales and describing their evolution influenced by small loop production and gravitational effects.

Contribution

It presents a novel analytical framework capturing non-linear dynamics of cosmic strings with non-scaling loops using a single parameter, simplifying complex interactions.

Findings

Predicts emergence of two new length scales: coherence length and cross-correlation length.

Shows that the parameter N grows logarithmically at late times due to cosmological effects.

Suggests late-time evolution may be affected by gravitational back-reaction scale.

Abstract

At early stages the dynamics of cosmic string networks is expected to be influenced by an excessive production of small loops at the scales of initial conditions l_{min}. To understand the late time behavior we propose a very simple analytical model of strings with a non-scaling population of loops. The complicated non-linear dynamics is described by only a single parameter N ~ 2/(1-C(l_{min})) where C(l) is a correlation function of the string tangent vectors. The model predicts an appearance of two new length scales: the coherence length \xi ~ t/N^2 and the cross-correlation length \chi ~ t/N. At the onset of evolution N ~ 10 and at late times N is expected to grow logarithmically due to cosmological stretching and emission of small loops. The very late time evolution might be modified further when the gravitational back-reaction scale grows larger than l_{min}.