Conformal quantum cosmology: Integrable models and Friedmann observables

The conformal-symmetry principle is used to construct integrable models of quantum cosmology that have a direct bearing on the observational cosmology with redshift and the Hubble law. Conformal-invariant field variables allo w us to establish a relation between standard cosmological models and actio n functionals appearing in quantum field theory. The conformal-symmetry pri nciple eliminates the Higgs potential from the Weinberg-Salam model and inc ludes the Penrose-Chernikov-Tagirov term. In the conformal version of the S tandard Model of electroweak interaction unified with Einstein gravity, the Higgs field is absorbed by the space metric, so that elementary-particle m asses and the evolution of the Universe have the same origin. In the flat-s pace limit, the a version of the Weinberg-Salam model without Higgs particl e-like excitations is obtained.