  We assume the validity of the Standard Model up to an arbitrary high-energy
scale and discuss what information on the early stages of the Universe can be
extracted from a measurement of the Higgs mass. For Mh < 130 GeV, the Higgs
potential can develop an instability at large field values. From the absence of
excessive thermal Higgs field fluctuations we derive a bound on the reheat
temperature after inflation as a function of the Higgs and top masses. Then we
discuss the interplay between the quantum Higgs fluctuations generated during
the primordial stage of inflation and the cosmological perturbations, in the
context of landscape scenarios in which the inflationary parameters scan. We
show that, within the large-field models of inflation, it is highly improbable
to obtain the observed cosmological perturbations in a Universe with a light
Higgs. Moreover, independently of the inflationary model, the detection of
primordial tensor perturbations through the B-mode of CMB polarization and the
discovery of a light Higgs can simultaneously occur only with exponentially
small probability, unless there is new physics beyond the Standard Model.
