The Boundary Proposal
The universe begins with a spacelike spherical boundary, not no boundary.
Looping ambient scene for Quantum Tunneling Origin. 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.
§1 · The claim, 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.
§2 · Why it might be true
Hassfeld and Hebecker 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.
§2.5 · Evidence
- Hassfeld & Hebecker (2024) show the proposal yields a finite, normalisable path integral where the no-boundary state runs into difficulties for landscape-like potentials.
§3 · What you'd need to test it
- Distinct primordial perturbation spectrum from Hartle-Hawking and Vilenkin proposals
- Specific signatures in the CMB tied to the boundary geometry
§4 · Where it breaks
- 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.
Go deeper
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.
The technical move that distinguishes the boundary proposal from Hartle-Hawking lies in the sign of the Euclidean action. In the no-boundary proposal, the wavefunction of the universe is computed as a path integral over compact Euclidean four-geometries with no boundary, weighted by exp(minus the Euclidean action). The integrand sign is set by Wick rotation from Lorentzian signature, and for landscape-like potentials with positive cosmological constant, this sign produces a divergent measure that favors empty de Sitter over universes with structure. Hassfeld and Hebecker's boundary proposal flips the integration contour so the path integral is weighted by exp(plus the Euclidean action) on a finite spacelike sphere, which is the Linde-Vilenkin sign convention extended to a sphere of arbitrary radius. The resulting measure is finite and normalisable, and the dominant saddle point corresponds to a universe with parameters matching observational cosmology rather than to the no-structure de Sitter background that pathologises Hartle-Hawking. The cost is that the boundary radius must be specified as input rather than emerging from the formalism.
Variants in this family
▸§5 · Who built it, and when(1 source, 1 established)
Up next
Spotted an error? Have a source to add?
Prefer email?
You can also send a prefilled email with the variant URL already filled in.