Hartle-Hawking No-Boundary
The universe has no temporal boundary, time itself emerged from a smooth Euclidean cap.
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
The universe has no temporal boundary at the beginning. In Euclidean time, the universe is a smooth four-dimensional surface with no edge, like asking what is south of the South Pole.
The claim
Hartle and Hawking proposed in 1983 that the universe's wavefunction is given by a path integral over all compact Euclidean four-geometries with no boundary. In Euclidean (imaginary) time, the universe is a smooth four-dimensional surface that smoothly caps off, like the rounded bottom of a sphere.
There is no "moment of creation" because there is no temporal boundary. Asking what happened before the Big Bang is, in this framework, like asking what is south of the South Pole. Time emerges as we move away from the Euclidean cap into Lorentzian (real-time) signature.
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
- No initial singularity
- Universe wavefunction smooth at a = 0
- Predicts a specific spectrum of cosmological perturbations
Evidence
- Elegant mathematical formulation
- Eliminates singularity problem
- Predicts de Sitter-like beginning compatible with inflation
Counterpoints
- Feldbrugge, Lehners, Turok (2017) argue the proposal predicts an unstable universe
- Direction of "outgoing" vs "incoming" mode is contested
- Picard-Lefschetz analysis suggests deeper problems
- Maldacena (2024) re-examines the no-boundary proposal and finds it predicts spatial curvature in conflict with observations, and is non-normalizable for landscape-like potentials.
- Ivo, Li & Maldacena (2024) show that tracing out unobserved regions of the no-boundary state yields phenomenologically unacceptable density matrices, sharpening the case against the original proposal.
Variants in this family
▸Go deeperTechnical detail with proper terminology
In the no-boundary proposal, the wavefunction of the universe is given by a Euclidean path integral over compact four-manifolds with the present three-geometry as the only boundary. There is no initial three-geometry; the path integral closes off smoothly at small a.
In Lorentzian signature, the universe emerges from the Euclidean region and evolves classically. The proposal is closely related to Vilenkin's but with a different choice of contour: Hartle-Hawking selects a no-boundary condition, Vilenkin selects an outgoing tunneling condition.
Recent work (Feldbrugge, Lehners, Turok 2017, 2018) using Picard-Lefschetz theory suggests that with proper definition of the path integral, the no-boundary proposal predicts perturbation amplitudes that grow exponentially, an unstable universe. This is hotly debated.
References
- EstablishedHartle & Hawking (1983). Phys. Rev. D 28, 2960
- EstablishedHawking (1984). Nucl. Phys. B 239, 257
- DebatedFeldbrugge, Lehners, Turok (2017). Phys. Rev. Lett. 119, 171301
- DebatedMaldacena (2024) Comments on the no boundary wavefunction and slow roll inflation66 citations
- DebatedIvo, Li & Maldacena (2024) The no boundary density matrix33 citations
Last reviewed May 14, 2026
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