Particlelike solutions in modified gravity: The Higgs monopole

Abstract

Higgs inflation has received 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 Füzfa et al. [Phys. Rev. Lett. 111, 12 (2013)]. 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 us 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.

Mimicking dark matter in Horndeski gravity

“…Any modified theory of gravity that does not violate the very stringent Solar System constraints should be taken seriously and tested at other scales. For example, the gravitational model of Higgs inflation [9] was studied in the context on compact object solutions [10] showing that it is negligibly different from GR around stellar compact objects.…”

Particle like solutions in modified gravity: the Higgs monopoles

“…Particlelike solutions in modified gravity: the Higgs monopoles Sandrine Schlögel We notice that mass and compactness of monopole plotted on Fig.2 do not correspond to a physical object. Actually, we can show that it is not possible to find a combination of physical parameters which gives rise to a monopole solution [5] for SM potential parameters. Indeed, for astrophysical objects, h c −→ 1, so we observe no deviation from GR even for large ξ .…”

“…In the following, we will focus on observational constraint of Higgs inflation in cosmology, thanks to CMB observations by Planck, and in astrophysics. We will show that Higgs inflation predicts particlelike solutions around compact objects, which we dubbed Higgs monopoles [4,5] since it consists in isolated compact objects charged under the Higgs field.…”

Self-gravitating spherical solutions of the nonminimally coupled non-Abelian Higgs model

“…For this type of solution, the boundary conditions of the YMH fields are identical to those discussed in [5,6] where the gauge fields are not excited from the beginning. Our solution could therefore be interpreted as a gauged version of the lump constructed in [5,6] (the stictly compact star used [5,6] is here mimicked by a boson star in the thin wall limit). Setting for definiteness α = 0.0001, we were able to construct the solutions for large values of −ξ.…”

“…First and foremost is the impact of the non-minimal coupling on smaller scale structures from star-like objects to solitons. One such study [5,6] was carried out recently with the (quite expected) conclusion that the additional coupling has negligible effects on stellar structures or more specifically, on stars with global U(1) scalar "hair". This result holds even when the non minimal coupling parameter −ξ is as large as 10 4 as required by the Higgs inflation models.…”