The Boundary Proposal
The universe begins with a spacelike spherical boundary, not no boundary.
Placeholder for a 3D visualisation of Quantum Tunneling Origin. The interactive scene will land in Phase 3. This family represents the 'null answer' to the chapter question: that there was no spacetime, no fields, no 'before' in any coherent sense. Apply quantum mechanics to the origin of the universe itself. The result is a wavefunction over possible universes; ours is the one that emerged. Different variants disagree on the boundary condition.
In one sentence
An alternative to Hartle-Hawking and Vilenkin in which the universe begins with a finite spacelike spherical boundary that can dominate over the no-boundary instanton.
The claim
Hertog and collaborators propose a third quantum-cosmological boundary condition alongside Hartle-Hawking and Vilenkin. Instead of no boundary at all or a tunneling-from-nothing, the universe begins on a finite spacelike sphere with specified geometry.
Under the Linde-Vilenkin sign convention, this proposal can dominate over the original no-boundary instanton in the path integral, suggesting it may be the preferred initial state in quantum cosmology rather than a competing alternative.
The family stance
Either literally nothing (Vilenkin), or a state without a temporal boundary (Hartle-Hawking), or a zero-energy quantum fluctuation (Tryon). All deny that a classical "before" makes sense.
Predictions
- Distinct primordial perturbation spectrum from Hartle-Hawking and Vilenkin proposals
- Specific signatures in the CMB tied to the boundary geometry
Evidence
- Hertog et al. (2024) show the proposal yields a finite, normalisable path integral where the no-boundary state runs into difficulties for landscape-like potentials.
Counterpoints
- Requires specifying the boundary geometry as input, which some critics view as no improvement over the boundary conditions it replaces.
- The phenomenological implications are still being worked out and have not yet been compared to Planck data.
Variants in this family
▸Go deeperTechnical detail with proper terminology
The proposal is a response to Maldacena (2024) and Ivo-Li-Maldacena (2024) showing pathologies in the original Hartle-Hawking state. See arXiv:2403.18892 for the formal development.
References
- Needs verificationHertog et al. (2024) The Boundary Proposal13 citations
Last reviewed May 14, 2026
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