  We have recently suggested [1,2] that Inflation could have started in a local
minimum of the Higgs potential at field values of about $10^{15}-10^{17}$ GeV,
which exists for a narrow band of values of the top quark and Higgs masses and
thus gives rise to a prediction on the Higgs mass to be in the range 123-129
GeV, together with a prediction on the the top mass and the cosmological
tensor-to-scalar ratio $r$. Inflation can be achieved provided there is an
additional degree of freedom which allows the transition to a radiation era. In
[1] we had proposed such field to be a Brans-Dicke scalar. Here we present an
alternative possibility with an additional subdominant scalar very weakly
coupled to the Higgs, realizing an (inverted) hybrid Inflation scenario.
Interestingly, we show that such model has an additional constraint $m_H<125.3
\pm 3_{th}$, where $3_{th}$ is the present theoretical uncertainty on the
Standard Model RGEs. The tensor-to-scalar ratio has to be within the narrow
range $10^{-4}\lesssim r<0.007$, and values of the scalar spectral index
compatible with the observed range can be obtained. Moreover, if we impose the
model to have subplanckian field excursion, this selects a narrower range
$10^{-4} \lesssim r<0.001$ and an upper bound on the Higgs mass of about $m_H
<124 \pm 3_{th}$.
