Stability of the effective potential of the gauge-less top-Higgs model in curved spacetime

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.