Lorentzian Quantum Cosmology
read the original abstract
We argue that the Lorentzian path integral is a better starting point for quantum cosmology than the Euclidean version. In particular, we revisit the mini-superspace calculation of the Feynman path integral for quantum gravity with a positive cosmological constant. Instead of rotating to Euclidean time, we deform the contour of integration over metrics into the complex plane, exploiting Picard-Lefschetz theory to transform the path integral from a conditionally convergent integral into an absolutely convergent one. We show that this procedure unambiguously determines which semiclassical saddle point solutions are relevant to the quantum mechanical amplitude. Imposing "no-boundary" initial conditions, i.e., restricting attention to regular, complex metrics with no initial boundary, we find that the dominant saddle contributes a semiclassical exponential factor which is precisely the {\it inverse} of the famous Hartle-Hawking result.
This paper has not been read by Pith yet.
Forward citations
Cited by 4 Pith papers
-
Ordering-Independent Wheeler-DeWitt Equation for Flat Minisuperspace Models
Path-integral measures determine operator orderings for the Wheeler-DeWitt equation in flat minisuperspace models, with all consistent choices yielding identical physical observables via field redefinition Jacobians.
-
Birth of Inflationary Universes via Wineglass Wormholes and their No-Boundary Relatives
Wineglass wormholes with a local maximum in the scale factor mediate the birth of inflationary spacetimes and split into background plus no-boundary geometries at small axionic or magnetic charge.
-
How to tame your (black hole) saddles: Lessons from the Lorentzian Gravitational Path Integral
A Lorentzian path integral contour for charged AdS black holes selects a finite subset of complex saddles via Picard-Lefschetz theory, ensuring the semiclassical sum converges at finite β.
-
Resolving Degeneracies in Complex $\mathbb{R}\times S^3$ and $\theta$-KSW
Exact Airy-function evaluation of the Gauss-Bonnet mini-superspace path integral plus Picard-Lefschetz resolution of lapse degeneracies via complex (G ħ) deformation that alters the KSW condition.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.