Bouncing Unitary Cosmology I: Mini-Superspace General Solution

TL;DR

This paper introduces a quantum cosmology model with a unitary bounce that resolves singularities, allowing superpositions of the cosmological constant and resulting in a finite, well-behaved universe free of classical singularities.

Contribution

It presents a novel quantization of mini-superspace models that guarantees unitarity and finiteness, enabling superpositions of the cosmological constant and avoiding singularities.

Findings

Model exhibits superpositions of cosmological constant values

Solutions are singularity-free and well-behaved

Discovery of bound 'Efimov universe' states for negative cosmological constant

Abstract

We offer a new proposal for cosmic singularity resolution based upon a quantum cosmology with a unitary bounce. This proposal is illustrated via a novel quantization of a mini-superspace model in which there can be superpositions of the cosmological constant. This possibility leads to a finite, bouncing unitary cosmology. Whereas the usual Wheeler--DeWitt cosmology generically displays pathological behaviour in terms of non-finite expectation values and non-unitary dynamics, the finiteness and unitarity of our model are formally guaranteed. For classically singular models with a massless scalar field and cosmological constant, we show that well-behaved quantum observables can be constructed and generic solutions to the universal Schr\"{o}dinger equation are singularity-free. Generic solutions of our model displays novel features including: i) superpositions of values of the cosmological constant; ii) universal effective physics due to non-trivial self-adjoint extensions of the Hamiltonian; and iii) bound `Efimov universe' states for negative cosmological constant. The last feature provides a new platform for quantum simulation of the early universe. A companion paper provides detailed interpretation and analysis of particular cosmological solutions that display a cosmic bounce due to quantum gravitational effects, a well-defined FLRW limit far from the bounce, and a semi-classical turnaround point in the dynamics of the scalar field which resembles an effective inflationary epoch.