Dilatonic formulation for conducting cosmic string models

TL;DR

This paper introduces a dilatonic auxiliary field to reformulate elastic cosmic string models into a standardized form with a quadratic kinetic term and a non-linear potential, simplifying analysis and highlighting specific examples like the transonic string model.

Contribution

It presents a novel dilatonic formulation that converts complex elastic string Lagrangians into a standardized form with explicit potential energy functions.

Findings

Derived explicit form of the potential energy function for various models.

Applied the formulation to the transonic string model with a specific potential.

Showed how the reformulation simplifies the analysis of cosmic string models.

Abstract

It is shown how the the introduction of a suitably defined dilatonic auxiliary field, $\Phi$ say, makes it possible for the non-linear Lagrangian for a generic elastic string model, of the kind appropriate for representing superconducting cosmic strings, to be converted into a standardised form as the sum of a kinetic term that is just homogeneously quadratic in the relevant scalar phase gradient (as in a simple linear model) together with a potential energy term, $V$ say, that is specified as a generically non-linear function of $\Phi$. The explicit form of this function is derived for various noteworthy examples, of which the most memorable is that of the transonic string model, as characterised by a given mass scale, $m$ say, for which this potential energy density will be expressible in terms of the zero current limit value $\Phi_{_0}$ of $\Phi$ by $ V= {1\over 2} m \big(\Phi_{_0}^{-2} \Phi^2+ \Phi_{_0}^{2} \Phi^{-2} \big)$.