Abstract
The Hamiltonian for the time-dependent Schr\"odinger equation for matter fields derived from the Wheeler-DeWitt equation for a quantum minisuperspace cosmological model minimally coupled to free massive minimal scalar fields consists of a set of parameter-dependent and implicitly cosmological time-dependent harmonic oscillators. By using the generalized invariant method we obtain the exact quantum states whose number states at an earlier gravitational configuration in an expanding stage get evolved unitarily by a squeeze operator into the same number states at the later identical gravitational configuration in the subsequent recollapsing stage. It is proposed that during an expansion and the subsequent recollapse of the Universe following a wide class of wave functions of the quantum minisuperspace cosmological model, the cosmological entropy production determined by the squeeze parameters may break the symmetry of the thermodynamic time.
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