Quantum Creation of the Universe: Reassessing the No-Boundary and Tunneling Proposals

How was our Universe created? This is one of the most fundamental questions in cosmology. Quantum cosmology attempts to answer it by using a "wave function of the Universe," and for four decades the discussion has been dominated by two proposals: the no-boundary proposal of Hartle and Hawking, and the tunneling proposal of Vilenkin. The two predict very different initial states for our Universe, yet for a long time there was no common framework in which they could be exactly analyzed and compared.

In this talk I will begin with a pedagogical introduction to the wave function of the Universe and to the Lorentzian path integral formulation based on Picard-Lefschetz theory, which makes the gravitational path integral well defined without the ambiguities of the traditional Euclidean approach and allows both proposals to be treated on the same footing. I will then present our recent results. Using Lefschetz-thimble analysis together with resurgence theory, we resolve the Stokes-line ambiguity that had obscured earlier analyses and show that the path integral uniquely yields the tunneling wave function rather than the no-boundary one. The no-boundary saddles nevertheless leave a trace: their contributions exactly cancel the Borel ambiguity of the perturbative quantum-gravity corrections around the tunneling saddle, demonstrating that resurgence is at work in quantum cosmology. I will also discuss what changes beyond general relativity, using Hořava-Lifshitz gravity as a concrete UV-complete example.