Lorentzian Quantum Cosmology

Understand

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.