The No-Boundary Proposal as a Path Integral with Robin Boundary Conditions

Abstract

Realising the no-boundary proposal of Hartle and Hawking as a consistent gravitational path integral has been a long-standing puzzle. In particular, it was demonstrated by Feldbrugge et al. that the sum over all universes starting from zero size results in an unstable saddle point geometry. Here we show that in the context of gravity with a positive cosmological constant, path integrals with a specific family of Robin boundary conditions overcome this problem. These path integrals are manifestly convergent and are approximated by stable Hartle-Hawking saddle point geometries. The price to pay is that the off-shell geometries do not start at zero size. The Robin boundary conditions may be interpreted as an initial state with Euclidean momentum, with the quantum uncertainty shared between initial size and momentum.

5 pages, 3 figures, v2: replaced with published version

References in corpus (2)

• No Rescue for the No Boundary Proposal
• The Real No-Boundary Wave Function in Lorentzian Quantum Cosmology

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• The no-boundary proposal in biaxial Bianchi IX minisuperspace
• Surprises in Lorentzian path-integral of Gauss-Bonnet gravity
• Revisiting the no-boundary proposal with a scalar field
• Generalized boundary conditions in closed cosmologies
• Anisotropic n-dimensional quantum cosmological model with fluid
• Aspects of Quantum Cosmology