A Boltzmann treatment for the vorton excess problem

TL;DR

This paper develops a comprehensive Boltzmann equation framework to model the evolution of current-carrying cosmic string loops, including vortons, accounting for gravitational waves, finite lifetimes, and various initial conditions.

Contribution

It introduces a generalized Boltzmann approach to study the cosmological evolution of vortons, extending previous models by incorporating detailed phase space dynamics and diverse physical effects.

Findings

Derived a three-dimensional phase space Boltzmann equation for vortons

Included effects of gravitational wave emission and finite vorton lifetime

Generalized previous models to track sub-populations over time

Abstract

We derive and solve a Boltzmann equation governing the cosmological evolution of the number density of current carrying cosmic string loops, whose centrifugally supported equilibrium configurations are also referred to as vortons. The phase space is three-dimensional and consists of the time variable, the loop size, and a conserved quantum number. Our approach includes gravitational wave emission, a possibly finite lifetime for the vortons and works with any initial loop distribution and for any loop production function. We then show how our results generalize previous approaches on the vorton excess problem by tracking down the time evolution of the various sub-populations of current-carrying loops in a string network.