  The lore paradigm for solving so-called horizon and flatness problems in
cosmology is the primordial inflation. Plethora of inflationary models have
been built in last decades and first experimental probes seem to appear in
favor of the inflationary paradigm. We will focus here on one of them, the
Higgs inflation, and show the combined constraint required for such a model at
cosmological as well as gravitational scales, i.e. for compact objects. We will
show that Higgs inflation model gives rise to particlelike solutions around
compact objects, dubbed Higgs monopoles, characterized by the nonminimal
coupling parameter as well as the mass and the compactness of the object. For
large values of the nonminimal coupling constant and specific compactness, the
amplitude of the Higgs field inside the matter distribution can be arbitrarily
large.
