Wheeler--DeWitt Universe Wave Function in the Presence of Stiff Matter

Abstract

We study the Wheeler-DeWitt (WDW) equation close to the Big-Bang. We argue that an interaction dominated fluid (speed of sound equal to the speed of light), if present, would dominate during such an early phase. Such a fluid with p = ρ ∝ 1/a 6 generates a term in the potential of the wave function of the WDW equation proportional to −1/a 2 . This very peculiar quantum potential, which embodies a spontaneous breaking of dilatation invariance, has some very remarkable consequences for the wave function of the Universe: Ψ(a) vanishes at the Big-Bang: Ψ(0) = 0; the wave function Ψ(a) is always real; a superselection rule assures that the system is confined to a ≥ 0 without the need of imposing any additional artificial barrier for unphysical negative a. These results do not depend on the operator-ordering problem of the WDW equation.