  We investigated inflation in the Higgs-$R^2$ model and assumed the trajectory
to follow a single-field approximation called minimal two-field mode. Using
this approximation, we tried to constrain the Higgs' non-minimal coupling
$\xi$. During inflation, we investigated the effect of $\xi$ on the
non-gaussianity. We found that $\xi$ could not provide the large
non-gaussianity. In this paper, we divided the preheating stage to be quadratic
regime and quartic regime. During the quadratic regime, the gauge bosons'
production is the most dominant. However, it could not drain the whole
inflaton's energy. Thus, we introduced a dark matter candidate with a large
coupling that could drain the whole inflaton's energy. We also found that if
$\xi<4.2$, the oscillation on the quadratic regime continued to the quartic
regime. The reheating temperature obtained by this mode can be reached to be
$\sim 10^{10}$ GeV and strongly depends on the remaining inflaton's energy
density. On contrary, if $\xi>4.2$, the oscillation only happens at the
quadratic regime. As we assumed the Pauli exclusion principle does exist during
the quadratic regime, the instant decay of gauge bosons to fermions is
restricted. Hence we expected, the reheating temperature to be low for about
$\sim 10^9$ GeV.
