Cold, warm, and composite (cool) cosmic string models

Abstract

The dynamical behaviour of a cosmic string is strongly affected by any reduction of the effective string tension $T$ below the constant value $T=m^2$ say that characterizes the simple, longitudinally Lorentz invariant, Goto Nambu string model in terms of a fixed mass scale $m$ whose magnitude depends on that of the Higgs field responsible for the existence of the string. Such a reduction occurs in the standard "hot" cosmic string model in which the effect of thermal perturbations of a simple Goto Nambu model is expressed by the formula $T^2=m^2(m^2-2πΘ^2/3)$, where $Θ$ is the string temperature. A qualitatively similar though analytically more complicated tension reduction phenomenon occurs in "cold" conducting cosmic string models where the role of the temperature is played by an effective chemical potential $μ$ that is constructed as the magnitude of the phase $ϕ$ of a bosonic condensate of the kind whose existence was first proposed by Witten. The present article describes the construction and essential mechanical properties of a category of "warm" cosmic string models that are intermediate between these "hot" and "cold" extremes. These "warm" models are the string analogues of the standard Landau model for a 2-constituent finite temperature superfluid, and as such involve two independent currents interpretable as that of the entropy on one hand and that of the bosonic condensate on the other. It is surmised that the stationary (in particular ring) equilibrium states of such "warm" cosmic strings may be of cosmological significance.