Quantum gravity corrections to the standard model Higgs in Einstein and $R^2$ gravity

We evaluate quantum gravity corrections to the standard model Higgs potential $V(phi)$ a la Coleman-Weinberg and examine the stability question of $V(phi)$ at scales of Planck mass $M_{rm Pl}$. We compute the gravity one-loop corrections by using the momentum cut-off in Einstein gravity. The gravity corrections affect the potential in a significant manner for the value of $Lambda= (1 - 3)M_{rm Pl}.$ In view of reducing the UV cut-off dependence we also make a similar study in the $R^2$ gravity.