No-boundary Wave Function, Wheeler-DeWitt Equation and Path Integral Analysis of the Bouncing `Quantum' Cosmology

TL;DR

This paper explores quantum cosmology of bouncing universe models, deriving analytical solutions using Wheeler-DeWitt and path integral methods, including a no-boundary wavefunction analogue and scalar perturbations.

Contribution

It introduces two analytically tractable bouncing models and develops their quantum descriptions via Wheeler-DeWitt and path integral approaches, including a no-boundary wavefunction analogue.

Findings

Derived a bouncing model analogue of the no-boundary wavefunction.

Presented a Lorentzian path integral representation for the model.

Discussed the inclusion of real scalar perturbations.

Abstract

Bouncing models are alternatives to inflationary cosmology that replace the initial Big-Bang singularity by a `bouncing' phase. A deeper understanding of the initial conditions of the universe, in these scenarios, requires knowledge of quantum aspects of bouncing models. In this work, we propose two classes of bouncing models that can be studied with great analytical ease and hence, provide test-bed for investigating more profound problems in quantum cosmology of bouncing universes. Our model's two key ingredients enable us to do straightforward analytical calculations: (i) a convenient parametrization of the minisuperspace of FRLW spacetimes and (ii) two distinct choices of the effective perfect fluids that source the background geometry of the bouncing universe. We study the quantum cosmology of these models using both the Wheeler-de Witt equations and the path integral approach. In particular, we found a bouncing model analogue of the no-boundary wavefunction and presented a Lorentzian path integral representation for the same. We also discuss the introduction of real scalar perturbations.