Is the Lorentzian no-boundary wave function well defined and stable?
In plain words
James Hartle and Stephen Hawking, two theoretical physicists, proposed that the universe began without any boundary in time, in the way the surface of a sphere has no edge at its pole. Recent calculations disagree on whether this proposal gives a sensible universe or one with uncontrollably large ripples.
Precise statement
For minisuperspace gravity with a positive cosmological constant plus linear tensor perturbations, evaluate the no-boundary amplitude as a Lorentzian path integral over the lapse using Picard-Lefschetz theory (deforming the integration contour onto steepest-descent paths). Feldbrugge, Lehners and Turok (2017, PRL 119, 171301) find unsuppressed perturbations; Diaz Dorronsoro, Halliwell, Hartle, Hertog and Janssen (2017, PRD 96, 043505) choose a contour giving a real wave function with suppressed, nearly Gaussian perturbations. Determine whether a physical principle (Wheeler-DeWitt equation with specified boundary conditions, unitarity, or a quantum-gravity completion) singles out one contour, and whether perturbations are suppressed for it.
What would settle it
A derivation of the contour from a principle accepted by both sides, followed by the computation of the tensor perturbation amplitude on that contour.
Status in the literature
Unverified note
The 2017 dispute is unresolved; 2024 to 2026 work in Jackiw-Teitelboim gravity, spin foams and lattice Lefschetz-thimble studies has not produced consensus.