Exact Solutions Of The Wheeler-Dewitt Equation With Ordering Term In A Dark Energy Scenario

We investigate the quantum evolution of the universe in the presence of two types of dark energies. First, we consider the phantom class (omega < -1) which would be responsible for a super-accelerated cosmic expansion, and then we apply the procedure to an ordinary A > 0 vacuum (omega = -1). This is done by analytically solving the Wheeler-DeWitt equation with ordering term (WdW) in the cosmology of Friedmann-Robertson-Walker. In this paper, we find exact solutions in the scale factor a and the ordering parameter q. For q = 1 it is shown that the universe has a high probability of evolving from a big bang singularity. On the other hand, for q = 0 the solution indicates that an initial singularity is unlikely. Instead, the universe has maximal probability of starting with a finite well-defined size which we compute explicitly at primordial times. We also study the time evolution of the scale factor by means of the Hamilton-Jacobi equation and show that an ultimate big rip singularity emerges explicitly from our solutions. The phantom scenario thus predicts a dramatic end in which the universe would reach an infinite scale factor in a finite cosmological time as pointed by Caldwell et al. in a classical setup (Caldwell et al., 2003). Finally, we solve the WdW equation with ordinary constant dark energy and show that in this case the universe does not rip apart in a finite era. (C) 2020 Elsevier B.V. All rights reserved.