Cosmic strings in the Abelian Higgs model with conformal coupling to gravity

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 Bogomol'nyi 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.