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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 applythis formulation to the inflationary cosmology driven by the Standard Model(SM) Higgs boson playing the role of an inflaton with a strong non-minimalcoupling to gravity. In this way a complete cosmological scenario is obtained,which embraces the formation of initial conditions for the inflationarybackground in the form of a sharp probability peak in the distribution of theinflaton field and the ongoing generation of the Cosmic Microwave Background(CMB) spectrum on this background. Formation of this probability peak is basedon the same RG mechanism which underlies the generation of the CMB spectrumwhich was recently shown to be compatible with the WMAP data in the Higgs massrange $135.6 {\rm GeV} \lesssim M_H\lesssim 184.5 {\rm GeV}$. This brings tolife a convincing unification of quantum cosmology with the particlephenomenology of the SM, inflation theory, and CMB observations.

Tunneling cosmological state revisited: Origin of inflation with a non-minimally coupled Standard Model Higgs inflaton