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We investigate gravitational effects on the so-called multiple pointcriticality principle (MPCP) at the Planck scale. The MPCP requires twodegenerate vacua, whose necessary conditions are expressed by vanishing Higgsquartic coupling $\lambda(M_{\rm Pl})=0$ and vanishing its $\beta$ function$\beta_\lambda(M_{\rm Pl})=0$. We discuss a case that a specific form ofgravitational corrections are assumed to contribute to $\beta$ functions ofcoupling constants although it is accepted that gravitational corrections donot alter the running of the standard model (SM) couplings. To satisfy theabove two boundary conditions at the Planck scale, we find that the top polemass and the Higgs mass should be $170.8\,{\rm GeV} \lesssim M_t\lesssim171.7\,{\rm GeV}$ and $M_h=125.7\pm0.4\,{\rm GeV}$, respectively, as well asinclude suitable magnitude of gravitational effects (a coefficient ofgravitational contribution as $|a_\lambda| > 2$). In this case, however, sincethe Higgs quartic coupling $\lambda$ becomes negative below the Planck scale,two vacua are not degenerate. We find that $M_h \gtrsim 131.5\,{\rm GeV}$ with$M_t \gtrsim 174\,{\rm GeV}$ is required by the realization of the MPCP.Therefore, the MPCP at the Planck scale cannot be realized in the SM and alsothe SM with gravity since $M_h \gtrsim 131.5\,{\rm GeV}$ is experimentallyruled out.

Gravitational effects on vanishing Higgs potential at the Planck scale