A Background Independent Algebra in Quantum Gravity

TL;DR

This paper introduces a background-independent algebra of operators in quantum gravity along an observer's worldline, linking it to the Hartle-Hawking state and defining entropy via relative entropy, especially in de Sitter vacua.

Contribution

It proposes a novel algebraic framework for quantum gravity that is background-independent and connects it to entropy definitions using the Hartle-Hawking state.

Findings

Defines a background-independent algebra of operators in quantum gravity.

Relates the Hartle-Hawking state to maximum entropy.

Provides sensible entropy results for de Sitter vacua.

Abstract

We propose an algebra of operators along an observer's worldline as a background-independent algebra in quantum gravity. In that context, it is natural to think of the Hartle-Hawking no boundary state as a universal state of maximum entropy, and to define entropy in terms of the relative entropy with this state. In the case that the only spacetimes considered correspond to de Sitter vacua with different values of the cosmological constant, this definition leads to sensible results.