  We pursued the question of the influence of a strong gravitational field on
the structure of the Higgs effective potential in the gauge-less top-Higgs
sector of the Standard Model with an additional scalar singlet. To this end, we
calculated the one-loop corrected effective potential in an arbitrary curved
spacetime. We have found that the gravity induced terms in the effective
potential may influence its behavior in both small and large field regions.
This result indicated the necessity of a more careful investigation of the
effect of high curvature in the problems concerning the stability of the Higgs
effective potential in the full Standard Model.
