Tunneling wave function of the universe

Abstract

The tunneling wave function of the universe is investigated in a minisuperspace framework of a de Sitter universe with a quantum scalar field, treated as a perturbation. We consider three different approaches to defining the tunneling wave function: (1) tunneling boundary conditions in superspace, (2) Lorentzian path integral, and (3) quantum tunneling from initial universe of a vanishing size. We show that the superspace approach requires Robin boundary conditions for the scalar field modes, the path integral approach requires adding an appropriate boundary term to the scalar field action, and the initial universe approach requires the initial quantum state of the scalar field to be Euclidean vacuum. We find that all three approaches yield identical wave functions and that scalar field fluctuations are well behaved, contrary to earlier claims in the literature.

17 pages; v2: typos fixed, published version

References in corpus (3)

• No Rescue for the No Boundary Proposal
• The Real No-Boundary Wave Function in Lorentzian Quantum Cosmology
• Damped perturbations in the no-boundary state

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