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Journal Article

Lorentzian Quantum Cosmology

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Lehners,  Jean-Luc
String Cosmology, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1703.02076.pdf
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Citation

Feldbrugge, J., Lehners, J.-L., & Turok, N. (2017). Lorentzian Quantum Cosmology. Physical Review D, 95: 103508. doi:10.1103/PhysRevD.95.103508.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-0A4F-9
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.