Higgs boson, renormalization group, and naturalness in cosmology
  We consider the renormalization group improvement in the theory of the
Standard Model (SM) Higgs boson playing the role of an inflaton with a strong
non-minimal coupling to gravity. At the one-loop level with the running of
constants taken into account, it leads to a range of the Higgs mass that is
entirely determined by the lower WMAP bound on the cosmic microwave background
(CMB) spectral index. We find that the SM phenomenology is sensitive to current
cosmological data, which suggests to perform more precise CMB measurements as a
SM test complementary to the LHC program. By using the concept of a
field-dependent cutoff, we show the naturalness of the gradient and curvature
expansion in this model within the conventional perturbation theory range of
the SM. We also discuss the relation of these results to two-loop calculations
and the limitations of the latter caused by parametrization and gauge
dependence problems.
