Kinetic Theory and Hydrodynamics of Cosmic Strings

TL;DR

This paper develops a kinetic theory for cosmic string networks, deriving transport and hydrodynamic equations that incorporate string interactions, gravitational effects, and equilibrium conditions, providing a comprehensive framework for large-scale string evolution.

Contribution

It introduces a detailed kinetic and hydrodynamic model for cosmic strings, including equilibrium conditions and the transition to non-equilibrium states.

Findings

Derived a transport equation for cosmic strings with Nambu-Goto dynamics.

Established conditions for thermodynamic equilibrium and characterized it using von Mises-Fisher distributions.

Formulated hydrodynamic equations governing large-scale string evolution.

Abstract

We develop further a kinetic theory of strings and derive a transport equation for a network of cosmic strings with Nambu-Goto evolution, interactions and background gravitational effects taken into account. We prove an H-theorem and obtain necessary and sufficient conditions for a thermodynamic equilibrium. At the lowest order the equilibrium is estimated by the von Mises-Fisher distributions parametrized by mean directions and dispersions of the right- and left-moving tangent vectors. Under assumption of a local equilibrium we derive a complete set of hydrodynamic equations that govern the evolution of strings on large scales. We also argue that on small scales the assumption of a local equilibrium would break down, and non-equilibrium steady states, described by the Sinai-Ruelle-Bowen distributions, should be used instead.