Running Non-Minimal Inflation with Stabilized Inflaton Potential
  In the context of the Higgs model involving gauge and Yukawa interactions
with the spontaneous gauge symmetry breaking, we consider $\lambda \phi^4$
inflation with non-minimal gravitational coupling, where the Higgs field is
identified as inflaton. Since the inflaton quartic coupling is very small, once
quantum corrections through the gauge and Yukawa interactions are taken into
account, the inflaton effective potential most likely becomes unstable. In
order to avoid this problem, we need to impose stability conditions on the
effective inflaton potential, which lead to not only non-trivial relations
amongst the particle mass spectrum of the model, but also correlations between
the inflationary predictions and the mass spectrum. For concrete discussion, we
investigate the minimal $B-L$ extension of the Standard Model with
identification of the $B-L$ Higgs field as inflaton. The stability conditions
for the inflaton effective potential fix the mass ratio amongst the $B-L$ gauge
boson, the right-handed neutrinos and the inflaton. This mass ratio also
correlates with the inflationary predictions. In other words, if the $B-L$
gauge boson and the right-handed neutrinos are discovered in future, their
observed mass ratio provides constraints on the inflationary predictions.
