2017/03/06 by Job Feldbrugge, Jean-Luc Lehners, Neil Turok · 227 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Classical mechanics #Cosmology and Gravitation Theories #Feynman diagram #Geometry #Loop quantum gravity #Mathematical analysis #Mathematical physics #Mathematics #Minisuperspace #Noncommutative and Quantum Gravity Theories #Path integral formulation #Physics #Quantum #Quantum cosmology #Quantum dynamics #Quantum gravity #Quantum mechanics #Quantum process #Saddle point #Semiclassical gravity #Semiclassical physics #Spin foam #Theoretical physics #Wheeler–DeWitt equation #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.95.103508
published in Physical review. D/Physical review. D. 95(10) (American Physical Society) · 44 pages, 8 figures
arxiv created 2017/03/06 · openalex publication_date 2017/05/16 · arxiv updated 2017/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We argue that the Lorentzian path integral is a better starting point for quantum cosmology than its Euclidean counterpart. In particular, we revisit the minisuperspace 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 inverse of the famous Hartle-Hawking result.