  The present measurement of the standard model (SM) parameters suggests that
the Higgs effective potential has a maximum at the intermediate scale, and the
electroweak (EW) vacuum is not absolutely stable. The simplest possibility for
absolute EW stability may be introducing a very large Higgs-Ricci scalar
non-minimal coupling. In this extension of the SM, I study the cosmic inflation
driven by the Higgs field. Since the resulting Hubble parameter happens to be
around the weak scale, I call this scenario $weak\text{-}scale\text{
}Higgs\text{ }inflation$. It is pointed out that the cosmic-microwave
background normalization of the scalar density perturbation can be enhanced
compared with the conventional Higgs inflation prediction, thanks to the
potential maximum predicted by the SM. It turns out in the Palatini formulation
of the gravity with various higher dimensional terms suppressed by the scale
close to the Planck scale that the inflation is successful, with a prediction
of the running of the spectral index, $\alpha_s=-(3-4)\times 10^{-3}$, which
can be tested in the future. I also argue the UV (in)sensitivity of the
prediction, the fact that the parameter region for successful inflation is very
close to the criticality for potential shapes for eternal and non-eternal
inflation, and the phenomenological applications.
