Probing singularities in quantum cosmology with curvature scalars

TL;DR

This paper demonstrates that quantum cosmological models, analyzed through the DeBroglie-Bohm interpretation, show finite curvature scalars at all times, providing evidence that quantum effects remove classical Big Bang singularities.

Contribution

It introduces the computation of local expectation values of curvature scalars in quantum FRW models, showing they remain finite and thus support singularity resolution.

Findings

Curvature scalars are finite at all times in quantum models.

Quantum effects eliminate classical Big Bang singularity.

Supports the hypothesis that quantum cosmology resolves singularities.

Abstract

We provide further evidence that the canonical quantization of cosmological models eliminates the classical Big Bang singularity, using the {\it DeBroglie-Bohm} interpretation of quantum mechanics. The usual criterion for absence of the Big Bang singularity in Friedmann-Robertson-Walker quantum cosmological models is the non-vanishing of the expectation value of the scale factor. We compute the `local expectation value' of the Ricci and Kretschmann scalars, for some quantum FRW models. We show that they are finite for all time. Since these scalars are elements of general scalar polynomials in the metric and the Riemann tensor, this result indicates that, for the quantum models treated here, the `local expectation value' of these general scalar polynomials should be finite everywhere. Therefore, we have further evidence that the quantization of the models treated here eliminates the classical Big Bang singularity. PACS: 04.40.Nr, 04.60.Ds, 98.80.Qc.