Wormholes, Classical Limit and Dynamical Vacuum in Quantum Cosmology

TL;DR

This paper explores quantum cosmological models with scalar fields and cosmological constants, revealing wormhole states and classical-quantum transition behaviors, and demonstrating that wormholes are common in such models.

Contribution

It introduces a quantization of FRW universes with scalar fields, finding wormhole states and classical-quantum transition phenomena, and shows wormholes are prevalent in simple matter quantum cosmology.

Findings

Discrete wormhole quantum states in closed models

States with classical behavior at small scale factors

Finite-norm wormhole solutions with definite cosmological constants

Abstract

First a Friedmann-Robertson-Walker (FRW) universe filled with dust and a conformally invariant scalar field is quantized. For the closed model we find a discrete set of wormhole quantum states. In the case of flat spacelike sections we find states with classical behaviour at small values of the scale factor and quantum behaviour for large values of the scale factor. Next we study a FRW model with a conformally invariant scalar field and a nonvanishing cosmological constant dynamically introduced by regarding the vacuum as a perfect fluid. The ensuing Wheeler-DeWitt equation turns out to be a bona fide Schrodinger equation, and we find that there are realizable states with a definite value of the cosmological constant. Once again we find finite-norm solutions to the Wheeler-DeWitt equation with definite values of the cosmological constant that represent wormholes, suggesting that in quantum cosmological models with a simple matter content wormhole states are a common occurrence.