Superconducting cosmic string: Equation of state for spacelike and timelike current in the neutral limit

Abstract

The equation of state relating the tension T and the energy per unit length U of a cosmic strin gis investigated in the simplest nontrivial case, namely, that of a field theory with invariance, in four dimensions, which is interpretable as the zero-charge-coupling-constant limit of the more general superconducting string models that have been previously investigated. This limit has the advantage of giving vacuum vortex defects that are strictly local so that the quantities such as U and T that are relevant for the macroscopic description can be computed without ambiguity.In the case of "electricn states (with timelike current) for which no comparable previous calculations exist, it is shown there is a critical frequency w c beyond which the vortex becomes unstable due to "charge" carrier emission. In the case of "magnetic" states (with spacelike current), the present analysis provides more precise results than those of previous investigations, whose predictions are broadly confirmed for typical moderate models in which the tension T remains comparable to the energy density U though not for extreme models, in which serious discrepancies are revealed. PACS number(s): 98.80.Cq, 11.17.t~ I N T R O D U C T I O NT h e purpose of this work is t o derive the macroscopic quantities characterizing t h e dynamics of a currentcarrying cosmic-string model of a charge-uncoupled or neutral kind whose complexity is intermediate between t h a t of t h e original nonconducting kind proposed by Kibble [l] and t h a t of t h e charge-coupled current-carrying kind proposed by Witten [2]. T h e most significantly new feature of this work is a first quantitative investigation of "electric" states, meaning those for which the current is timelike whereas previous numerical results (confirmed in moderate situations by t h e more precise numerical method used here) were restricted t o "magnetic" states, meaning those for which the current is spacelike. One of t h e reasons why only a very few authors [3,4] have paid much attention t o "electricn-type states was the consideration t h a t t h e corresponding electromagnetic fields would tend t o b e screened. However, more recent discussions [5] have made t h e point t h a t the most important effects of currents in cosmic strings are mechanical rather t h a n electromagnetic a n d as such can b e studied even in the neutral (&coupled) limit t o which the present work is restricted.Early discussions of t h e potential astrophysical significance of strings of t h e latter kind concentrated on spectacular effects (such as the formation of cosmological voids [6]) t h a t might have been expected as a consequence of electromagnetic radiation resulting from the charge coupling of t h e currents. However it later became apparent t h a t t h e most important effects of currents in cosmic strings are of a purely mechanical nature, a n d can b e analyzed as a first approximation in terms of cosmicstring models of t h e simpler kind considered here, which are t o b e interpreted as corresponding t o t...

Equation of state of cosmic strings with fermionic current carriers

“…This limit, for which the coupling between fermions and electromagnetic-like external fields is made to vanish, permits an easy recognition of the dynamical effects of the existence of an internal structure as in Ref. [14].…”

“…Moreover, it is interesting to compute the electromagnetic-like fermionic current, its scalar analogue being involved in the equation of state for a cosmic string with bosonic current carriers [14]. From an additional global U (1) invariance of the Lagrangian, the electromagnetic-like current takes similar form as the vectorial one coupled to the string gauge field.…”

“…For scalar as well as vector carriers, the task of understanding the microphysics is made simple thanks to their bosonic nature: all the trapped particles go into the same lowest accessible energy state and the field can be treated classically [13,14]. Even the surrounding electromagnetic [15] and gravitational [16,17] fields generated by the current can be treated this way and the backreaction can be included easily [18].…”

“…Such a formalism relied heavily on the fact that for a bosonic carrier, the relevant quantity whose variation along the string leads to a current is its phase, and the state parameter is essentially identifiable to this phase gradient. Various equations of state relating the tension to the energy per unit length were then derived [20], based on numerical results and the existence of a phase frequency threshold [14]. It even includes the special case of a chiral current [21], although the latter originates in principle only for a purely fermionic current.…”

“…In the last section (section V), the classical expressions for the energy per unit length and the tension are derived and discussed from computation of quantum observable values of the stress tensor operator in the classical limit. Contrary to the bosonic current-carrier case where there is only one state parameter [14], the classical limit of the model involves four state parameters in order to fully determine the energy per unit length and the tension. The cosmological consequences of this new analysis are briefly discussed in the concluding section.…”