Wheeler-DeWitt Universe Wave Function in the presence of stiff matter

TL;DR

This paper investigates the Wheeler-DeWitt equation near the Big Bang in the presence of a stiff matter fluid, revealing a quantum potential that causes the wave function to vanish at the singularity and enforces a superselection rule for the scale factor.

Contribution

It introduces a novel quantum potential from stiff matter that affects the universe's wave function, ensuring it vanishes at the Big Bang and is always real, independent of operator ordering.

Findings

Wave function vanishes at the Big Bang ($=0$).

Wave function remains real throughout.

Superselection rule confines the universe to non-negative scale factors.

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 $p=\rho\propto1/a^{6}$ 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: $\Psi(a)$ vanishes at the Big-Bang: $\Psi(0)=0$; the wave function $\Psi(a)$ is always real; a superselection rule assures that the system is confined to $a\geq0$ 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.