Lessons for quantum cosmology from anti-de Sitter black holes

TL;DR

This paper explores how insights from anti-de Sitter black holes and their thermodynamics can inform quantum cosmology, especially regarding the no-boundary proposal and universe nucleation, through gravitational path integrals with boundary conditions.

Contribution

It demonstrates the application of AdS black hole thermodynamics to quantum cosmology, analyzing path integrals with boundary conditions and complex saddle points, linking AdS and dS spaces.

Findings

Hawking-Page transition is recovered in the model.

Below a minimum temperature, saddle points become complex.

Finite cutoff introduces suppressed additional saddle points.

Abstract

Gravitational physics is arguably better understood in the presence of a negative cosmological constant than a positive one, yet there exist strong technical similarities between the two settings. These similarities can be exploited to enhance our understanding of the more speculative realm of quantum cosmology, building on robust results regarding anti-de Sitter black holes describing the thermodynamics of holographic quantum field theories. To this end, we study 4-dimensional gravitational path integrals in the presence of a negative cosmological constant, and with minisuperspace metrics. We put a special emphasis on boundary conditions and integration contours. The Hawking-Page transition is recovered and we find that below the minimum temperature required for the existence of black holes the corresponding saddle points become complex. When the asymptotic anti-de Sitter space is cut off at a finite distance, additional saddle points contribute to the partition function, albeit in a very suppressed manner. These findings have direct consequences for the no-boundary proposal in cosmology, because the anti-de Sitter calculation can be brought into one-to-one correspondence with a path integral for de Sitter space with Neumann conditions imposed at the nucleation of the universe. Our results lend support to recent implementations of the no-boundary proposal focusing on momentum conditions at the "big bang".