Phantom energy versus cosmological constant: Comparative results via analytical solutions of the Wheeler-DeWitt equation (original) (raw)

In the present paper, we investigate how the phantom class of dark energy, presumably responsible for a super-accelerated cosmic expansion and here described by the state parameter ω=-5/3, determines the wave function of the Universe. This is done by analytically solving the Wheeler-DeWitt (WdW) equation in the cosmology of Friedmann-Robertson-Walker with an ambiguity term arising from the ordering of the conjugate operators associated with the scale factor a. Its solutions depend on an additional parameter q related to that ordering and show that the Universe presents maximal probability to come into existence with a well-defined size for q = 0. The amplitude of the wavefunction is higher the higher is the phantom energy content so an initial singularity of the type a = 0 is very unlikely. In this semi-classical approach, we also study how the scale factor evolves with time via the Hamilton-Jacobi equation assuming a flat Universe. We show that the ultimate big rip singularity emer...