nLab no boundary proposal

Idea

The Hartle-Hawking no-boundary-proposal in quantum cosmology [Hawking 1982, Hartle & Hawking 1983] is the informal assertion that wavefunctions $\Psi(X^3, g)$ on the space of spatial cosmological geometries $(X^3,g)$ are given by the path integral over all (partially Wick-rotated) 4d geometries whose only boundary is $X^3$, hence which have no boundary in the past.

The idea is that this describes quantum states of the universe for those cosmological evolutions where the universe appears “out of nothing”.

References

The original articles:

• S. W. Hawking, The Boundary Conditions of the Universe, Pontif. Acad. Sci. Scr. Varia 48 (1982) 563–574

• J. B. Hartle, S. W. Hawking, Wave function of the Universe, Phys. Rev. D 28 2960 (1983) [doi:10.1103/PhysRevD.28.2960]

• S. W. Hawking, section 3 of: The Nature of Space and Time [arXiv:hep-th/9409195]

Review and further discussion:

• Jean-Luc Lehners, Review of the No-Boundary Wave Function, Physics Reports 1022 (2023) 1-82 [arXiv:2303.08802, doi:10.1016/j.physrep.2023.06.002]

• Juan Maldacena, Comments on the no boundary wavefunction and slow roll inflation [arXiv:2403.10510]

• Wikipedia, Hartle-Hawking state

See also:

• Victor Ivo, Yue-Zhou Li, Juan Maldacena: The no boundary density matrix [arXiv:2409.14218]