  If the Standard Model is valid up to very high energies it is known that the
Higgs potential can develop a local minimum at field values around
$10^{15}-10^{17}$ GeV, for a narrow band of values of the top quark and Higgs
masses. We show that in a scalar-tensor theory of gravity such Higgs false
vacuum can give rise to viable inflation if the potential barrier is very
shallow, allowing for tunneling and relaxation into the electroweak scale true
vacuum. The amplitude of cosmological density perturbations from inflation is
directly linked to the value of the Higgs potential at the false minimum.
Requiring the top quark mass, the amplitude and spectral index of density
perturbations to be compatible with observations, selects a narrow range of
values for the Higgs mass, $m_H=126.0\pm 3.5$ GeV, where the error is mostly
due to the theoretical uncertainty of the 2-loop RGE. This prediction could be
soon tested at the Large Hadron Collider. Our inflationary scenario could also
be further checked by better constraining the spectral index and the
tensor-to-scalar ratio.
