Quantum cosmology and late-time singularities

TL;DR

This paper reviews classical and quantum cosmological models with soft and exotic singularities, analyzing their classification, behavior, and quantum modifications, including effects on the universe's evolution and initial quantum states.

Contribution

It provides a comprehensive classification and analysis of soft and exotic singularities in cosmology, incorporating quantum effects and brane-world scenarios, which is a novel synthesis.

Findings

Quantum corrections can alter the nature of soft singularities.

Scalar field models exhibit phantom divide line crossing.

Quantum cosmology with density matrix states offers new insights.

Abstract

The development of dark energy models has stimulated interest to cosmological singularities, which differ from the traditional Big Bang and Big Crunch singularities. We review a broad class of phenomena connected with soft cosmological singularities in classical and quantum cosmology. We discuss the classification of singularities from the geometrical point of view and from the point of view of the behaviour of finite size objects, crossing such singularities. We discuss in some detail quantum and classical cosmology of models based on perfect fluids (anti-Chaplygin gas and anti-Chaplygin gas plus dust), of models based on the Born-Infeld-type fields and of the model of a scalar field with a potential inversely proportional to the field itself. We dwell also on the phenomenon of the phantom divide line crossing in the scalar field models with cusped potentials. Then we discuss the Friedmann equations modified by quantum corrections to the effective action of the models under considerations and the influence of such modification on the nature and the existence of soft singularities. We review also quantum cosmology of models, where the initial quantum state of the universe is presented by the density matrix (mixed state). Finally, we discuss the exotic singularities arising in the brane-world cosmological models.