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, $musimeq M_{rm Pl}$ ($M_{rm Pl}=1.22times10^{19}{rm GeV}$). 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 $M_{rm Pl}$.