Title: Recent Developments in Quantum Cosmology

Abstract: After a brief overview of the concepts behind quantum cosmology, with an emphasis on the no-boundary proposal for the very early universe, I will present the Kontsevich-Segal criterion. Kontsevich and Segal have proposed a constraint on complex metrics by demanding the path integral of p-form fields to converge on a given fixed background. Witten has conjectured that this constraint could apply to quantum gravity path integrals. The consequences for quantum cosmology have thus been explored in the last couple of years. I will review some of these recent developments, including classical and quantum (tunnelling) transitions of the universe. More emphasis will be given on the Hartle-Hawking no-boundary proposal, where it is found that flatter potentials more easily satisfy the Kontsevich-Segal bound. When taking into account the weighting of the wave function, which favours nucleation at low values on the inflationary potential, the effects conspire to suggest that only a minimal amount of inflation could have occurred. This, in turn, points towards our universe today being relatively small.

Talk – Slides

Talk – Video