  Apparent metastability of the electroweak vacuum poses a number of
cosmological questions. These concern evolution of the Higgs field to the
current vacuum, and its stability during and after inflation. Higgs-inflaton
and non-minimal Higgs-gravity interactions can make a crucial impact on these
considerations potentially solving the problems. In this work, we allow for
these couplings to be present simultaneously and study their interplay. We find
that different combinations of the Higgs-inflaton and non-minimal Higgs-gravity
couplings induce effective Higgs mass during and after inflation. This
crucially affects the Higgs stability considerations during preheating. In
particular, a wide range of the couplings leading to stable solutions becomes
allowed.
