  In the present paper we develop a model of the Higgs inflation based on the
non-minimal coupling of the Higgs boson to gravity predicted by Graviweak
Unification. But later we get rid of the non-minimal coupling to gravity by
making the conformal transformation from the Jordan frame to the Einstein
frame. We construct a self-consistent $Spin(4,4)$-invariant model of the
unification of gravity with weak $SU(2)$ interactions in the assumption of the
existence of visible and invisible sectors of the Universe. Assuming the
interaction between the ordinary and mirror Higgs fields, we develop a special
Hybrid model of inflation. According to this model, the inflaton starts trapped
from the "false vacuum" of the Universe at the Higgs field VEV $v\sim 10^{18}$
GeV (in the visible world). Then the inflations of the two Higgs doublet
fields, visible $\phi$ and mirror $\phi'$, lead to the emergence of the
Standard Model vacua at the Electroweak scales with the Higgs boson VEVs
$v_1\approx 246$ GeV and $v'_1=\zeta v_1$ in the visible and invisible worlds,
respectively. Considering the results of cosmology and calculating the number
of e-folds $N^*$, we predict $\zeta\simeq 100-115$ for $N^*\simeq 50-60$, in
agreement with previous results of the model with broken mirror parity. We also
consider RGEs, taking into account the mixing term - the interaction between
the ordinary and mirror Higgs bosons, assuming the smallness of the mixing
coupling.
