Abelian-Higgs strings in Rastall gravity

TL;DR

This study explores Abelian-Higgs cosmic strings within Rastall gravity, revealing how quantum effects influence string properties, including the deficit angle and supermassive solutions, with results derived through numerical solutions of modified equations.

Contribution

It introduces a phenomenological model of Abelian-Higgs strings in Rastall gravity, analyzing their properties and solutions without an action principle, highlighting differences from Einstein gravity.

Findings

Deficit angle increases as Rastall parameter decreases.

Supermassive string solutions with singularities occur at small parameters.

Energy per unit length can be proportional to winding number under certain conditions.

Abstract

In this paper we analyze Abelian-Higgs strings in a phenomenological model that takes quantum effects in curved space-time into account. This model, first introduced by Rastall, cannot be derived from an action principle. We formulate phenomenological equations of motion under the guiding principle of minimal possible deformation of the standard equations. We construct string solutions that asymptote to a flat space-time with a deficit angle by solving the set of coupled non-linear ordinary differential equations numerically. Decreasing the Rastall parameter from its Einstein gravity value we find that the deficit angle of the space-time increases and becomes equal to $2\pi$ at some critical value of this parameter that depends on the remaining couplings in the model. For smaller values the resulting solutions are supermassive string solutions possessing a singularity at a finite distance from the string core. Assuming the Higgs boson mass to be on the order of the gauge boson mass we find that also in Rastall gravity this happens only when the symmetry breaking scale is on the order of the Planck mass. We also observe that for specific values of the parameters in the model the energy per unit length becomes proportional to the winding number, i.e. the degree of the map $S^1 \rightarrow S^1$. Unlike in the BPS limit in Einstein gravity, this is, however, not connect to an underlying mathematical structure, but rather constitutes a would-be-BPS bound.