We suggest a path integral formulation for the tunneling cosmological state,
which admits a consistent renormalization and renormalization group (RG)
improvement in particle physics applications of quantum cosmology. We apply
this formulation to the inflationary cosmology driven by the Standard Model
(SM) Higgs boson playing the role of an inflaton with a strong non-minimal
coupling to gravity. In this way a complete cosmological scenario is obtained,
which embraces the formation of initial conditions for the inflationary
background in the form of a sharp probability peak in the distribution of the
inflaton field and the ongoing generation of the Cosmic Microwave Background
(CMB) spectrum on this background. Formation of this probability peak is based
on the same RG mechanism which underlies the generation of the CMB spectrum
which was recently shown to be compatible with the WMAP data in the Higgs mass
range 135.6GeV≲MH≲184.5GeV. This brings to
life a convincing unification of quantum cosmology with the particle
phenomenology of the SM, inflation theory, and CMB observations.Comment: 18 pages, 3 figures, LaTe