Particlelike solutions in modified gravity: the Higgs monopole
  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.
