  We discuss the lower Higgs boson mass bounds which come from the absolute
stability of the Standard Model (SM) vacuum and from the Higgs inflation, as
well as the prediction of the Higgs boson mass coming from asymptotic safety of
the SM. We account for the 3-loop renormalization group evolution of the
couplings of the Standard Model and for a part of two-loop corrections that
involve the QCD coupling alpha_s to initial conditions for their running. This
is one step above the current state of the art procedure ("one-loop
matching--two-loop running"). This results in reduction of the theoretical
uncertainties in the Higgs boson mass bounds and predictions, associated with
the Standard Model physics, to 1-2 GeV. We find that with the account of
existing experimental uncertainties in the mass of the top quark and alpha_s
(taken at 2sigma level) the bound reads M_H>=M_min (equality corresponds to the
asymptotic safety prediction), where M_min=129+-6 GeV. We argue that the
discovery of the SM Higgs boson in this range would be in agreement with the
hypothesis of the absence of new energy scales between the Fermi and Planck
scales, whereas the coincidence of M_H with M_min would suggest that the
electroweak scale is determined by Planck physics. In order to clarify the
relation between the Fermi and Planck scale a construction of an
electron-positron or muon collider with a center of mass energy ~200+200 GeV
(Higgs and t-quark factory) would be needed.
