  The Higgs-inflaton coupling plays an important role in the Higgs field
dynamics in the early Universe. Even a tiny coupling generated at loop level
can have a dramatic effect on the fate of the electroweak vacuum. Such
Higgs-inflaton interaction is present both at the trilinear and quartic levels
in realistic reheating models. In this work, we examine the Higgs dynamics
during the preheating epoch, focusing on the effects of the parametric and
tachyonic resonances. We use lattice simulations and other numerical tools in
our studies. We find that the resonances can induce large fluctuations of the
Higgs field which destabilize the electroweak vacuum. Our considerations thus
provide an upper bound on quartic and trilinear interactions between the Higgs
and the inflaton. We conclude that there exists a favourable range of the
couplings within which the Higgs field is stabilized during both inflation and
preheating epochs.
