  In scalaron-Higgs inflation the Standard Model Higgs boson is non-minimally
coupled to gravity and the Einstein-Hilbert action is supplemented by the
quadratic scalar curvature invariant. For the quartic Higgs self-coupling
$\lambda$ fixed at the electroweak scale, we find that the resulting
inflationary two-field model effectively reduces to a single field model with
the same predictions as in Higgs inflation or Starobinsky inflation, including
the limit of a vanishing non-minimal coupling. For the same model, but with the
scalar field a priori not identified with the Standard Model Higgs boson, we
study the inflationary consequences of an extremely small $\lambda$. Depending
on the initial conditions for the inflationary background trajectories, we find
that the two-field dynamics either again reduces to an effective single-field
model with a larger tensor-to-scalar ratio than predicted in Higgs inflation
and Starobinsky inflation, or involves the full two-field dynamics and leads to
oscillatory features in the inflationary power spectrum. Finally, we
investigate under which conditions the inflationary scenario with extremely
small $\lambda$ can be realized dynamically by the Standard Model
renormalization group flow and discuss how the scalaron-Higgs model can provide
a natural way to stabilize the electroweak vacuum.
