Tunneling cosmological state and the origin of Higgs inflation in the standard model

For the tunneling cosmological state, we propose a path integral formulation admitting a consistent renormalization and renormalization-group improvement in particle physics applications of quantum cosmology with heavy massive quantum fields. We apply this formulation to the inflationary cosmology driven by the standard-model Higgs boson playing the role of an inflaton with a strong nonminimal coupling to gravity. A complete cosmological scenario is thus obtained, embracing 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 spectrum on this background. We also discuss the status of the no-boundary and tunneling states in a cosmology driven by massless fields conformally coupled to gravity.