Quantum Cosmology and Open Universes

TL;DR

This paper investigates quantum creation of universes with different curvatures, showing that quantum effects favor open universes and predict sufficient inflation, thus providing insights into the initial conditions and evolution of the cosmos.

Contribution

It demonstrates that quantum cosmology favors open universes and predicts sufficient inflation, with modifications to the Wheeler De Witt equation's superpotential.

Findings

Quantum cosmology favors open ($k=-1$) universes.

The wavefunction's behavior differs for open and flat cases.

Sufficient inflation (~60 e-foldings) is predicted in all cases.

Abstract

Quantum creation of Universes with compact spacelike sections that have curvature $k$ either closed, flat or open, i.e. $k=\pm1,0$ are studied. In the flat and open cases, the superpotential of the Wheeler De Witt equation is significantly modified, and as a result the qualitative behaviour of a typical wavefunction differs from the traditional closed case. Using regularity arguments, it is shown that the only consistent state for the wavefunction is the Tunneling one. By computing the quantum probabilities for the curvature of the sections, it is shown that quantum cosmology actually favours that the Universe be open, $k=-1$. In all cases sufficient inflation $\sim 60$ e-foldings is predicted: this is an improvement over classical measures that generally are ambiguous as to whether inflation is certain to occur.