  In previous publications we have proposed that Inflation can be realized in a
second minimum of the Standard Model Higgs potential at energy scales of about
$10^{16}$ GeV, if the minimum is not too deep and if a mechanism which allows a
transition to the radiation dominated era can be found. This is provided, {\it
e.g.}, by scalar-tensor gravity models or hybrid models. Using such ideas we
had predicted the Higgs boson mass to be of about $126\pm 3$ GeV, which has
been confirmed by the LHC, and that a possibly measurable amount of gravity
waves should be produced. Using more refined recent theoretical calculations of
the RGE we show that such scenario has the right scale of Inflation only for
small Higgs mass, lower than about 124 GeV, otherwise gravity waves are
overproduced. The precise value is subject to some theoretical error and to
experimental errors on the determination of the strong coupling constant. Such
an upper bound corresponds also to the recent claimed measurement by BICEP2 of
the scale of inflation through primordial tensor modes. Finally we show that
introducing a moderately large non-minimal coupling for the Higgs field the
bound can shift to larger values and be reconciled with the LHC measurements of
the Higgs mass.
