Stephen Hawking estava errado: espaço-tempo era infinito no Big Bang

sexta-feira, junho 16, 2017

Lorentzian quantum cosmology

Job Feldbrugge, Jean-Luc Lehners, and Neil Turok

Phys. Rev. D 95, 103508 – Published 16 May 2017


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.

Received 22 March 2017

© 2017 American Physical Society