## 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 Schrodinger 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.

Original language | English |
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Article number | 035009 |

Number of pages | 32 |

Journal | Classical and Quantum Gravity |

Volume | 36 |

Issue number | 3 |

DOIs | |

Publication status | Published - 18-Jan-2019 |

## Keywords

- quantum cosmology
- singularity resolution
- cosmological constant
- problem of time
- bouncing cosmology
- GRAVITATIONAL COLLAPSE
- INFLATIONARY UNIVERSE
- COMPLETE OBSERVABLES
- HAWKING RADIATION
- QUANTUM
- TIME
- ANALOG
- SINGULARITIES
- EQUATIONS
- EVOLUTION