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.
