Gravity loop corrections to the standard model Higgs in Einstein gravity

We study one-loop quantum gravity corrections to the standard model Higgs potential $V(\phi)$ $\grave{\rm a}$ la Coleman-Weinberg and examine the stability question of $V(\phi)$ in the energy region of Planck mass scale, $\mu\simeq M_{\rm Pl}$ ($M_{\rm Pl}=1.22\times10^{19}{\rm GeV}$). We calculate the gravity one-loop corrections to $V(\phi)$ in Einstein gravity by using the momentum cut-off $\Lambda$. We have found that even small gravity corrections compete with the standard model term of $V(\phi)$ and affect the stability argument of the latter part alone. This is because the latter part is nearly zero in the energy region of $M_{\rm Pl}$.