Evolution in bouncing quantum cosmology
  We present the method of describing an evolution in quantum cosmology in the
framework of the reduced phase space quantization of loop cosmology. We apply
our method to the flat Friedman-Robertson-Walker model coupled to a massless
scalar field. We identify the physical quantum Hamiltonian that is
positive-definite and generates globally an unitary evolution of considered
quantum system. We examine properties of expectation values of physical
observables in the process of the quantum big bounce transition. The dispersion
of evolved observables are studied for the Gaussian state. Calculated relative
fluctuations enable an examination of the semi-classicality conditions and
possible occurrence of the cosmic forgetfulness. Preliminary estimations based
on the cosmological data suggest that there was no cosmic amnesia. Presented
results are analytical, and numerical computations are only used for the
visualization purposes. Our method may be generalized to sophisticated
cosmological models including the Bianchi type universes.
