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 \(M_{\rm Pl}\).