Quantum Gravity In De Sitter Space

TL;DR

This paper explores the properties and challenges of formulating quantum gravity in de Sitter space, emphasizing the finite-dimensional Hilbert space and the difficulties in defining measurable observables.

Contribution

It provides a definition of the quantum Hilbert space in de Sitter space based on asymptotic behavior and discusses the conceptual issues in measuring observables.

Findings

Hilbert space in de Sitter space is finite-dimensional

Challenges in defining measurable observables in asymptotically de Sitter spacetime

Meta-observables exist but are unmeasurable by local observers

Abstract

We discuss some general properties of quantum gravity in De Sitter space. It has been argued that the Hilbert space is of finite dimension. This suggests a macroscopic argument that General Relativity cannot be quantized -- unless it is embedded in a more precise theory that determines the value of the cosmological constant. We give a definition of the quantum Hilbert space using the asymptotic behavior in the past and future, without requiring detailed microscopic knowledge. We discuss the difficulties in defining any precisely calculable or measurable observables in an asymptotically de Sitter spacetime, and explore some meta-observables that appear to make mathematical sense but cannot be measured by an observer who lives in the spacetime. This article is an expanded version of a lecture at Strings 2001 in Mumbai.