Bouncing and Cyclic Quantum Primordial Universes and the Ordering Problem

TL;DR

This paper explores how different operator orderings in quantum cosmology affect the evolution of the early universe, revealing new bouncing and cyclic solutions in the non-trivial ordering case.

Contribution

It introduces an alternative non-trivial operator ordering in quantum cosmology and demonstrates its impact on universe evolution, including new bouncing and cyclic solutions.

Findings

Non-trivial ordering leads to new bouncing solutions.

Cyclic solutions are present in the non-trivial case.

Non-singular solutions remain valid across orderings.

Abstract

In a Bohmian quantum cosmology scenario, we investigate some quantum effects on the evolution of the primordial universe arising from the adoption of an alternative non-trivial ordering to the quantization of the constrained Hamiltonian of a minimally coupled scalar field. The Wheeler-DeWitt equation has a contribution from the change in factor ordering, hence there are new quantum effects. We compare the results between the non-trivial and the trivial ordering cases, showing that the classical limit is valid for both orderings, but new bouncing and cyclic solutions are present in the non-trivial case. Additionally, we show that the non-singular solutions already present in the trivial ordering formalism keep valid.