The enigmatic gravitational partition function

TL;DR

This paper critically examines the foundational aspects of gravitational partition functions, especially in de Sitter space, aiming to establish a more rigorous understanding of horizon entropy beyond saddle point approximations.

Contribution

It addresses foundational issues in quantum gravitational partition functions and explores a more solid theoretical basis for de Sitter horizon entropy.

Findings

Highlights limitations of saddle point approximation in quantum gravity

Proposes approaches for a more rigorous understanding of horizon entropy

Connects horizon entropy to the Hilbert space dimension in de Sitter space

Abstract

The saddle point approximation to formal quantum gravitational partition functions has yielded plausible computations of horizon entropy in various settings, but it stands on shaky ground. In this paper we visit some of that shaky ground, address some foundational questions, and describe efforts toward a more solid footing. We focus on the case of de Sitter horizon entropy which, it has been argued, corresponds to the dimension of the Hilbert space of a ball of space surrounded by the cosmological horizon.