Quantum Cosmology

TL;DR

This paper discusses the Hartle-Hawking no-boundary proposal in quantum cosmology, exploring its partial successes and new results in models with exponential scalar potentials, highlighting the complexity of summing over multiple extrema.

Contribution

It introduces new findings on the no-boundary wavefunction in models with exponential scalar potentials, expanding understanding of quantum cosmology solutions.

Findings

Partial validation of the no-boundary proposal in specific models

Identification of multiple complex extrema in exponential scalar potential models

Discussion of implications for quantum state of the universe

Abstract

A complete model of the universe needs at least three parts: (1) a complete set of physical variables and dynamical laws for them, (2) the correct solution of the dynamical laws, and (3) the connection with conscious experience. In quantum cosmology, item (2) is the quantum state of the cosmos. Hartle and Hawking have made the `no-boundary' proposal, that the wavefunction of the universe is given by a path integral over all compact Euclidean 4-dimensional geometries and matter fields that have the 3-dimensional argument of the wavefunction on their one and only boundary. This proposal is incomplete in several ways but also has had several partial successes, mainly when one takes the zero-loop approximation of summing over a small number of complex extrema of the action. This is illustrated here by the Friedmann-Robertson-Walker-scalar model. In particular, new results are discussed when the scalar field has an exponential potential, which generically leads to an infinite number of complex extrema among which to choose.