Physical aspects of unitary evolution of Bianchi-I quantum cosmological model

In this study, we examine some physical aspects of unitary evolution of the Bianchi-I model. In particular, we investigate the behavior of the volume and the scale factor as a function of time for the Bianchi-I universe with ultra-relativistic fluid (α = 1). The expectation value of volume is shown not to hit any singularity. We elucidate on the anisotropic nature of the solution and physically interpret the wavefunction as a superposition of collapsing universe and expanding universe mimicking Hartle–Hawking type wavefunction. The same analysis has been done for $\alpha \ne 1$ as well. This study also suggests  how to obtain the Vilenkin type wavefunction representing an expanding universe without it being superposed with a solution representing a collapsing universe. We also indicate a possible phase transition phenomenon for $\alpha \ne 1$ case with the existence of a critical parameter. (paper)