When do real observers resolve de Sitter's imaginary problem?

TL;DR

This paper investigates when real observers can resolve the imaginary phase in the Euclidean de Sitter path integral, revealing that only certain observers sharing specific fluctuations can eliminate the phase.

Contribution

It derives a general constraint on when real observers can reorganize the de Sitter phase, distinguishing gravitational from topological spectators and analyzing their capabilities.

Findings

Sector's infrared effective action being metric independent leads to phase persistence.

An information-bearing clock is necessary but not sufficient for phase removal.

Observers sharing negative modes of the conformal factor can remove the de Sitter phase.

Abstract

The universal phase $\rev{\ii}^{D+2}$ of the Euclidean de Sitter path integral obstructs a straightforward state-counting interpretation of the Gibbons--Hawking entropy. Building on Maldacena's proposal that specific black-hole observers can reorganize this phase, we derive a general constraint on when such ``real observers'' can succeed. By distinguishing \emph{gravitational observers} from \emph{topological spectators}, we show at quadratic semiclassical order that any sector whose \emph{infrared effective} action is metric independent at the de Sitter saddle factorizes in the path integral, $\Ztot = \Zgrav^{(\text{obs})}\Ztop$, so the imaginary phase persists regardless of the sector's information-processing capabilities. Using confining $\SU(3)$ gauge theory and topological orders as examples, we demonstrate that an information-bearing clock is necessary but insufficient: only observers whose fluctuations share the negative modes of the conformal factor belong to the special class that can remove the de Sitter phase.