Bouncing unitary cosmology I. Mini-superspace general solution

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 Schrödinger 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.

Superpositions of the cosmological constant allow for singularity resolution and unitary evolution in quantum cosmology

“…These generically cross the Rindler horizon at v = 0, which constitutes the boundary of configuration space. It can be shown, [21], that generic solutions tation and analysis of both general and particular cosmological solutions [21,22].…”

“…are bounded and essentially self-adjoint and, therefore, form an orthonormal basis for H according to the spectral theorem. For a geometric approach to this construction, see [21].…”

“…For Λ < 0, bound solutions can be constructed and are found to have discrete spectrum [21]. We will motivate excluding these solutions in the section on modelling constraints below.…”

“…Given the log-periodicity of Λ ref , the limit e |k0|/ e ω0/σω (21) implies that for any choice of Λ ref there is an equivalent one imperceptibly close to Λ 0 . The behaviour of the self-adjoint extensions is thus found to be universal in this limit.…”

Integrable minisuperspace models with Liouville field: energy density self-adjointness and semiclassical wave packets

“…Hence one classical action correspond to a family of distinct quantum models with different quantum evolutions. The cosmological models with similar self-adjointness issues were considered in [32,33].…”