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.