Top mass determination, Higgs inflation, and vacuum stability

The possibility that new physics beyond the Standard Model (SM) appears only at the Planck scale $M_P$ is often considered. However, it is usually argued that new physics interactions at $M_P$ do not affect the SM stability phase diagram, so the latter is obtained neglecting these terms. According to this diagram, for the current experimental values of the top and Higgs masses, our universe lives in a metastable state (with very long lifetime), near the edge of stability. Contrary to these expectations, however, we show that the stability phase diagram strongly depends on new physics and that, despite claims to the contrary, a more precise determination of the top (as well as of the Higgs) mass will not allow to discriminate between stability, metastability or criticality of the electroweak vacuum. At the same time, we show that the conditions needed for the realization of Higgs inflation scenarios (all obtained neglecting new physics) are too sensitive to the presence of new interactions at $M_P$. Therefore, Higgs inflation scenarios require very severe fine tunings that cast serious doubts on these models.