The Wave Function of Simple Universes, Analytically Continued From Negative to Positive Potentials

TL;DR

This paper explores the connection between AdS and dS universes through analytic continuation of the partition function, revealing insights into the no-boundary wave function and the emergence of time in quantum cosmology.

Contribution

It demonstrates a novel analytic continuation approach linking AdS and dS universes, clarifies the role of saddle points, and introduces a new no-boundary condition based on momentum flux.

Findings

Analytic continuation defines the no-boundary wave function in simple models.

Saddle points with tunneling geometries are irrelevant for universe nucleation.

Time emerges from space via a Stokes phenomenon in positive vacuum energy scenarios.

Abstract

We elaborate on the correspondence between the canonical partition function in asymptotically AdS universes and the no-boundary proposal for positive vacuum energy. For the case of a pure cosmological constant, the analytic continuation of the AdS partition function is seen to define the no-boundary wave function (in dS) uniquely in the simplest minisuperspace model. A consideration of the AdS gravitational path integral implies that on the dS side, saddle points with Hawking-Moss/Coleman-De Luccia-type tunnelling geometries are irrelevant. This implies that simple topology changing geometries do not contribute to the nucleation of the universe. The analytic AdS/dS equivalence holds up once tensor fluctuations are added. It also works, at the level of the saddle point approximation, when a scalar field with a mass term is included, though in the latter case, it is the mass that must be analytically continued. Our results illustrate the emergence of time from space by means of a Stokes phenomenon, in the case of positive vacuum energy. Furthermore, we arrive at a new characterisation of the no-boundary condition, namely that there should be no momentum flux at the nucleation of the universe.