Topological Higgs inflation: The origin of the Standard Model
  criticality
  The measured values of the Higgs and top masses and of the strong gauge
coupling constant point to the near-criticality of the Standard Model, where
two vacua at the electroweak and Planck scales are quasi-degenerate. We argue
that the criticality is required by the occurrence of an eternal topological
inflation induced by the Higgs potential. The role of this inflation is to
continuously create sufficiently flat and homogeneous Universe, providing the
necessary initial condition for the subsequent slow-roll inflation that
generates the density perturbations of the right magnitude. While the condition
for the topological Higgs inflation is only marginally satisfied in the
Standard Model, it can be readily satisfied if one introduces the right-handed
neutrinos and/or the non-minimal coupling to gravity; currently unknown quantum
gravity corrections to the potential may also help. We also discuss the $B-L$
Higgs inflation as a possible origin of the observed density perturbations. Its
necessary initial condition, the restored $B-L$ symmetry, can be naturally
realized by the preceding topological Higgs inflation.
