Lorentzian Quantum Cosmology

Job Feldbrugge, Jean-Luc Lehners, Neil Turok

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Article number103508
Pages (from-to)1-20
Number of pages20
JournalPhysical Review D
Issue number10
Publication statusPublished - 15 May 2017


  • hep-th
  • gr-qc


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