Consistent probabilities in loop quantum cosmology

TL;DR

This paper develops a consistent histories framework for loop quantum cosmology, demonstrating that the probability of a singularity is zero and a bounce occurs with probability one, providing a rigorous quantum cosmological analysis.

Contribution

It generalizes the consistent histories approach to loop quantum cosmology, explicitly computing probabilities for bounces versus singularities in an exactly solvable model.

Findings

Probability of singularity is zero for generic states.

Probability of a bounce is unity for generic states.

All states achieve arbitrarily large volume in infinite scalar time.

Abstract

A fundamental issue for any quantum cosmological theory is to specify how probabilities can be assigned to various quantum events or sequences of events such as the occurrence of singularities or bounces. In previous work, we have demonstrated how this issue can be successfully addressed within the consistent histories approach to quantum theory for Wheeler-DeWitt-quantized cosmological models. In this work, we generalize that analysis to the exactly solvable loop quantization of a spatially flat, homogeneous and isotropic cosmology sourced with a massless, minimally coupled scalar field known as sLQC. We provide an explicit, rigorous and complete decoherent histories formulation for this model and compute the probabilities for the occurrence of a quantum bounce vs. a singularity. Using the scalar field as an emergent internal time, we show for generic states that the probability for a singularity to occur in this model is zero, and that of a bounce is unity, complementing earlier studies of the expectation values of the volume and matter density in this theory. We also show from the consistent histories point of view that all states in this model, whether quantum or classical, achieve arbitrarily large volume in the limit of infinite `past' or `future' scalar `time', in the sense that the wave function evaluated at any arbitrary fixed value of the volume vanishes in that limit. Finally, we briefly discuss certain misconceptions concerning the utility of the consistent histories approach in these models.