Dynamics of Cosmic Strings and other Brane models

TL;DR

This paper develops a comprehensive theoretical framework for analyzing the dynamics of cosmic strings and branes, including their perturbations, stability, and equilibrium states in various background fields.

Contribution

It introduces a general geometric and dynamical model for branes, incorporating electromagnetic and Kalb-Ramond couplings, and explores stability and equilibrium configurations.

Findings

Propagation characteristics of small perturbations are determined by the surface stress tensor.

Special features of strings, including stable ring states, are analyzed using a quadratic Hamilton-Jacobi formulation.

The model applies to phenomena like superconducting cosmic strings and domain walls.

Abstract

The supporting worldsheet of a string, membrane, or other higher dimensional brane, is analysed in terms of its first, second, and third fundamental tensors, and its inner and outer curvature tensors. The dynamical equations governing the models appropriate for phenomena such as (superconducting) cosmic strings and cosmic domain walls are developed in a general framework (allowing for both electromagnetic and Kalb Ramond background coupling). It is shown how the surface stress momentum energy density tensor determines the propagation characteristics of small ``wiggle" perturbations of the worldsheet. Attention is then focussed on special features of strings (using the transonic model with tension T inversely proportional to the energy density U as a particularly important example). A quadratic Hamilton-Jacobi formulation is shown to govern equilibium states and other conservative string configurations sharing a symmetry of the (gravitational, electromagnetic, and Kalb-Ramond) background, including stable ring states that may be cosmologically important.