Asymptotic freedom in inflationary cosmology with a non-minimally
  coupled Higgs field
  We consider the renormalization group improvement in the theory of the
Standard Model Higgs boson playing the role of an inflaton with a strong
non-minimal coupling to gravity. It suggests the range of the Higgs mass $135.6
{\rm GeV} \lesssim M_H\lesssim 184.5 {\rm GeV}$ compatible with the current CMB
data (the lower WMAP bound on $n_s$), which is close to the widely accepted
range dictated by the electroweak vacuum stability and perturbation theory
bounds. We find the phenomenon of asymptotic freedom induced by this
non-minimal curvature coupling, which brings the theory to the weak coupling
domain everywhere except at the lower and upper boundary of this range. The
renormalization group running of the basic quantity ${\boldmath $A_I$}$ -- the
anomalous scaling in the non-minimally coupled Standard Model, which
analytically determines all characteristics of the CMB spectrum -- brings
${\boldmath $A_I$}$ to small negative values at the inflation scale. This
property is crucial for the above results and may also underlie the formation
of initial conditions for the inflationary dynamics in quantum cosmology.
