Semi-scaling cosmic strings

TL;DR

This paper presents a comprehensive analytical model of cosmic string network evolution, incorporating back-reaction effects from loops, and derives key distribution functions and correlation properties.

Contribution

It introduces a novel set of non-linear equations describing string dynamics with back-reaction, solved analytically for late-time behavior.

Findings

Correlation function is exponential.

Derived spectrum of scaling loops.

Analytical solutions for string distributions at late times.

Abstract

We develop a model of string dynamics with back-reaction from both scaling and non-scaling loops taken into account. The evolution of a string network is described by the distribution functions of coherence segments and kinks. We derive two non-linear equations which govern the evolution of the two distributions and solve them analytically in the limit of late times. We also show that the correlation function is an exponential, and solve the dynamics for the corresponding spectrum of scaling loops.