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

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arxiv 1903.06757 v2 pith:GZSD7XAL submitted 2019-03-15 hep-th gr-qc

Alice Di Tucci , Jean-Luc Lehners This is my paper · ORCID
classification hep-thgr-qc
keywords pathboundaryconditionsrobinsizegeometriesinitialintegral
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Small-Throat Boundary Condition for the Tunneling Wave Function of the Universe

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    Tunneling wave function of a closed universe is recovered as the ε o0 limit of a Neumann-plus-small-domain path integral with radiation-induced throat, excluding the unsuppressed outer saddle.

  2. Resolving Degeneracies in Complex $\mathbb{R}\times S^3$ and $\theta$-KSW

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    Exact Airy-function evaluation of the Gauss-Bonnet mini-superspace path integral plus Picard-Lefschetz resolution of lapse degeneracies via complex (G ħ) deformation that alters the KSW condition.

  3. Anisotropic quantum universe in Ho\v{r}ava-Lifshitz gravity

    gr-qc 2025-05 conditional novelty 6.0 of 10

    In the small-universe limit of Horava-Lifshitz gravity, the Wheeler-DeWitt equation separates and the anisotropy wave functions become normalizable harmonic-oscillator states, predicting small initial anisotropies set...

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