Cosmic Strings in the Abelian Higgs Model with Conformal Coupling to Gravity

TL;DR

This paper investigates cosmic string solutions within the abelian Higgs model when conformally coupled to gravity, highlighting key differences from minimal coupling and revealing new features and bounds related to the string's properties.

Contribution

It demonstrates the existence of cosmic string solutions with conformal coupling and analyzes their characteristics, contrasting them with minimally coupled solutions and identifying new bounds and features.

Findings

Absence of Bogomolnyi solutions with conformal coupling

Relation between angular deficit and magnetic field bounded by a critical value

New features of abelian Higgs cosmic strings with conformal coupling

Abstract

Cosmic string solutions of the abelian Higgs model with conformal coupling to gravity are shown to exist. The main characteristics of the solutions are presented and the differences with respect to the minimally coupled case are studied. An important difference is the absence of Bogomolnyi cosmic string solutions for conformal coupling. Several new features of the abelian Higgs cosmic strings of both types are discussed. The most interesting is perhaps a relation between the angular deficit and the central magnetic field which is bounded by a critical value.