Particlelike solutions in modified gravity: the Higgs monopole

TL;DR

This paper investigates particlelike solutions called Higgs monopoles within modified gravity theories, analyzing their properties, stability, and deviations from general relativity, especially focusing on effects of nonminimal coupling and potential resonances.

Contribution

It provides a detailed analytical and numerical study of Higgs monopoles in scalar-tensor gravity, revealing a resonance mechanism and conditions for regular solutions with minimal deviations from GR.

Findings

Higgs monopoles are the only regular asymptotically flat solutions with finite energy.

Deviations from GR are negligible for astrophysical bodies with standard model parameters.

A resonance mechanism can amplify the Higgs field, leading to potential divergences at certain parameters.

Abstract

Higgs inflation has received a remarkable attention in the last few years due to its simplicity and predictive power. The key point of this model is the nonminimal coupling to gravity in unitary gauge. As such, this theory is in fact a scalar-tensor modification of gravity that needs to be studied also below the energy scales of inflation. Motivated by this goal, we study in great analytical and numerical detail the static and spherically symmetric solutions of the equations of motion in the presence of standard baryonic matter, called "Higgs monopoles" and presented in 1305.2640. These particlelike solutions may arise naturally in tensor-scalar gravity with mexican hat potential and are the only globally regular asymptotically flat solutions with finite classical energy. In the case when the parameters of the potential are taken to be the ones of the standard model, we find that the deviations from general relativity are extremely small, especially for bodies of astrophysical size and density. This allows to derive a simplified description of the monopole, for which the metric inside the spherical matter distribution can be approximated by the standard metric of general relativity. We study how the properties of these monopoles depend on the strength of the nonminimal coupling to gravity and on the baryonic mass and compactness. An important and original result is the existence of a mechanism of resonant amplification of the Higgs field inside the monopole that comes into play for large nonminimal coupling. We show that this mechanism might degenerate into divergences of the Higgs field that reveal the existence of forbidden combinations of radius and baryonic energy density.