Gravity loop corrections to the standard model Higgs in Einstein gravity

We study one-loop quantum gravity corrections to the standard model Higgs potential $V(\varphi )$ $\grave{\mathrm{a}}$ la Coleman-Weinberg and examine the stability question of $V(\varphi )$ in the energy region of Planck mass scale, $\mu \simeq M_{\mathrm{P}\mathrm{l}}$ ($M_{\mathrm{P}\mathrm{l}}=1.22\times {10}^{19}\mathrm{G}\mathrm{e}\mathrm{V}$). We calculate the gravity one-loop corrections to $V(\varphi )$ in Einstein gravity by using the momentum cut-off $\mathrm{\Lambda }$. We have found that even small gravity corrections compete with the standard model term of $V(\varphi )$ and affect the stability argument of the latter part alone. This is because the latter part is nearly zero in the energy region of $M_{\mathrm{P}\mathrm{l}}$.