Orateur
Description
We introduce time as a “test field” in minisuperspace quantum cosmology. We argue that the time dependent wavefunction of the universe satisfies a Schrödinger equation and select solutions where the time field has negligible backreaction on the metric. By applying this idea to a radiation-dominated epoch, we model show that the problem reduces to that of a quantum particle in an $s$-wave state scattering off an attractive power-law potential $V(r)\sim -r^{-2/3}$. Quantum mechanically, this potential admits bound states and yields a smooth, unitary bounce—absent in the classical theory—where the uncertainty and expectation value of the scale factor are comparable. By choosing a large initial variance, the bounce can be made arbitrarily smooth, with a correspondingly soft evolution of the mean Hubble rate.
