De Sitter quantum gravity and the emergence of local algebras

TL;DR

This paper investigates how local physics emerges in perturbative quantum gravity around de Sitter space, showing that local algebras can be approximated in certain regions, with accuracy depending on the spacetime location.

Contribution

It introduces gauge-invariant observables that approximate local field algebras in de Sitter space, clarifying the conditions for locality emergence in quantum gravity.

Findings

Local algebra approximation is accurate near minimal $S^d$ for small time intervals.

Approximation remains accurate over large regions far in the future or past of the minimal $S^d$.

Large parts of static patches can be approximated by local algebras.

Abstract

Quantum theories of gravity are generally expected to have some degree of non-locality, with familiar local physics emerging only in a particular limit. Perturbative quantum gravity around backgrounds with isometries and compact Cauchy slices provides an interesting laboratory in which this emergence can be explored. In this context, the remaining isometries are gauge symmetries and, as a result, gauge-invariant observables cannot be localized. Instead, local physics can arise only through certain relational constructions. We explore such issues below for perturbative quantum gravity around de Sitter space. In particular, we describe a class of gauge-invariant observables which, under appropriate conditions, provide good approximations to certain algebras of local fields. Our results suggest that, near any minimal $S^d$ in dS$_{d+1}$, this approximation can be accurate only over regions in which the corresponding global time coordinate $t$ spans an interval $\Delta t \lesssim O(\ln G^{-1})$. In contrast, however, we find that the approximation can be accurate over arbitrarily large regions of global dS$_{d+1}$ so long as those regions are located far to the future or past of such a minimal $S^d$. This in particular includes arbitrarily large parts of any static patch.