  Gravitational freeze-in is a mechanism to explain the observed dark matter
relic density if dark matter neither couples to inflation nor to standard model
sector. In this work, we study gravitational freeze-in dark matter production
during Higgs preheating based on non-perturbative resonance. Using reliable
lattice method to handle this non-perturbative process, we show that tachyonic
resonance is prohibited by strong back reaction due to Higgs self interaction
needed to keep the positivity of potential during preheating, and parameter
resonance is viable by tuning the Higgs self-interaction coupling to be small
enough in ultraviolet energy scale. We then derive the dark matter relic
density under the context of Higgs preheating, and uncover a new dark matter
parameter space with dark matter mass larger than inflaton mass, which arises
from out-of-equilium Higgs annihilation. Finally, we briefly remark the open
question of testing gravitational dark matter.
