The logarithmic equation of state for superconducting cosmic strings

Abstract

This investigation follows up the suggestion that the equation of state for superconducting cosmic strings provided by Witten's prototype biscalar field model can be well represented by an effective Lagrangian of simple logarithmic form depending on only 3 independent parameters. The numerical work described here confirms the validity of this approximation, and initiates the evaluation of the 3 required parameters, as functions of the masses and other parameters specifying the underlying U(1) x U(1) scalar field model in the limit for which the relevant gauge coupling constants are small.In this limit, subject to calibration of the relevant length and mass scales, the scalar field model is characterised by just 3 dimensionless ratios which (in order to provide conducting strings) must be subject to three inequalities (of which two have obvious analytic expressions). It is found here that when all three of these inequalities are satisfied by a reasonably large margin, there is a simple empirical formula that can be used to provide a fairly accurate prescription for the algebraic dependence on these 3 dimensionless ratios of the 3 parameters required for the logarithmic equation of state.

15 pages including 5 figures; v2: notation used in eq. (6) clarified

References in corpus (8)

• Constraints on string networks with junctions
• Dynamical instability criterion for circular (vorton) string loops
• On the evolution of cosmic-superstring networks
• A practical model for cosmic (p,q) superstrings
• Avoidance of Collapse by Circular Current-Carrying Cosmic String Loops
• Dynamical Stability of Witten Rings
• Superconducting Electroweak Strings
• Generic Current-Carrying Strings

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• Stability and the equation of state for kinky vortons
• Shock waves in superconducting cosmic strings: growth of current
• Gravitating vortons as ring solitons in general relativity
• Gravitating superconducting strings with timelike or spacelike currents
• Can type II Semi-local cosmic strings form?
• Y-junction intercommutations of current carrying strings
• Fields in nonaffine bundles. III. Effective symmetries and conserved currents in strings and higher branes
• Stability of superconducting strings coupled to cosmic strings
• Fields in nonaffine bundles. IV. Harmonious non-Abelian currents in string defects
• Radial excitations of current-carrying vortices