Gaugeless reduction of gravity and the evolution of the Universe

The physical phase space of Einstein gravity with the Dirac-Arnowitt-Deser-Misner metric is constructed without using a gauge-fixing condition by explicitly resolving the constraints for nonphysical fields. As a result, from the reduced Einstein action we get a new energy-momentum tensor for independent dynamical fields. The corresponding energy and time are in direct analogy with the ‘‘spectral energy’’ and ‘‘observable time’’ for a relativistic particle. We discuss the photon and graviton excitations in the reduced theory and the ‘‘spectral history’’ of the evolution of the quantum Universe from inflation until the classical Friedman stage.