Quantum and classical properties of the Universe according to unimodular quantum cosmology

We investigate the dynamical behavior of wavepacket solutions due to unimodular quantum cosmology. We find early and late time quantum eras of the Universe. An Ehrenfest theorem ensures quasi-classical behavior for the late time Universe if the quantum uncertainties are small. The surprising prediction of late time quantum effects for a flat, homogeneous and isotropic Universe with a scalar field with an exponential potential is obtained by the analysis of the uncertainty dynamics using the results of the corresponding classical dynamical system. Furthermore quantum correction terms to the Hubble parameter and the matter density are derived. A positive matter expectation value for the de-Sitter Universe raises the question if correction terms due to quantum gravity could contribute to solve the dark matter problem.