Time and Entropy from Semi-classical Tunneling of the Cosmological Scale Function

Two major apparently unrelated problems, that of the origin of time in the universe associated with quantum gravity and of the entropy in de Sitter cosmological models, are found to have their origin in a single physical phenomenon: the semi-classical tunneling through a classically forbidden region of the cosmological scale factor. In this region there is a mixing of the states of quantum matter and those of the semi-classical gravity which produces a thermal mixture of the matter states and hence an ”entropy;” this same mixing effect brings about the conversion of a parametric time variable into a physical intrinsic time.