Singularities and Classical Limit in Quantum Cosmology

TL;DR

This paper investigates the classical and quantum behavior of minisuperspace models from string theories, revealing that quantum states are classical only at small scales and often exhibit initial singularities, with some special superpositions avoiding them.

Contribution

It provides a detailed analysis of classical and quantum solutions in quantum cosmology models, highlighting the behavior of wave functions and Bohmian trajectories near singularities.

Findings

Quantum states are sharply peaked around classical trajectories only for small scale factors.

Most Bohmian trajectories exhibit initial singularities, with some special superpositions avoiding them.

No non-singular trajectories grow to the size of the observable universe.

Abstract

Minisuperspace models derived from Kaluza-Klein theories and low energy string theory are studied. They are equivalent to one and two minimally coupled scalar fields. The general classical and quantum solutions are obtained. Gaussian superposition of WKB solutions are constructed. Contrarily to what is usually expected, these states are sharply peaked around the classical trajectories only for small values of the scale factor. This behaviour is confirmed in the framework of the causal interpretation: the Bohmian trajectories of many quantum states are classical for small values of the scale factor but present quantum behaviour when the scale factor becomes large. A consequence of this fact is that these states present an initial singularity. However, there are some particular superpositions of these wave functions which have Bohmian trajectories without singularities. There are also singular Bohmian trajectories with a short period of inflation which grow forever. We could not find any non-singular trajectory which grows to the size of our universe.