  We investigate stability of the Higgs effective potential in curved
spacetime. To this end, we consider the gauge-less top-Higgs sector with an
additional scalar field. Explicit form of the terms proportional to the squares
of the Ricci scalar, the Ricci tensor and the Riemann tensor that arise at the
one-loop level in the effective action has been determined. We have
investigated the influence of these terms on the stability of the scalar
effective potential. The result depends on background geometry. In general, the
potential becomes modified both in the region of the electroweak minimum and in
the region of large field strength.
