Holography of information in de Sitter space

TL;DR

<3-5 sentence high-level summary>We develop a gauge-fixed framework to define a natural norm on the space of Wheeler-DeWitt solutions in asymptotically de Sitter spacetimes, using a diff×Weyl Faddeev-Popov construction and a corresponding ghost sector. In the nongravitational limit, the norm reproduces Higuchi's group-averaged prescription, while in gravity it provides gravitational corrections to Higuchi and yields a robust, gauge-invariant notion of expectation values for cosmological correlators treated as gauge-fixed observables. A central result is a holography of information in de Sitter space: cosmological correlators in an arbitrarily small region determine the full quantum state, owing to the conformal symmetries encoded by the residual ${ m SO}(1,d+1)$ structure and the gauge constraints of gravity. These findings illuminate how gravitational Gauss laws constrain information localization and offer a precise, gauge-theoretic route to relate local observables to global state data in quantum cosmology.

Abstract

We study the natural norm on the space of solutions to the Wheeler-DeWitt equation in an asymptotically de Sitter spacetime. We propose that the norm is obtained by integrating the squared wavefunctional over field configurations and dividing by the volume of the diff-and-Weyl group. We impose appropriate gauge conditions to fix the diff-and-Weyl redundancy and obtain a finite expression for the norm using the Faddeev-Popov procedure. This leads to a ghost action that has zero modes corresponding to a residual conformal subgroup of the diff-and-Weyl group. By keeping track of these zero modes, we show that Higuchi's norm for group-averaged states emerges from our prescription in the nongravitational limit. We apply our formalism to cosmological correlators and propose that they should be understood as gauge-fixed observables. We identify the symmetries of these observables. In a nongravitational theory, it is necessary to specify such correlators everywhere on a Cauchy slice to identify a state in the Hilbert space. In a theory of quantum gravity, we demonstrate a version of the principle of holography of information: cosmological correlators in an arbitrarily small region suffice to completely specify the state.

Figures (2)

• Figure 1: The residual gauge group is the Euclidean conformal group in $d$ dimensions $\mathrm{SO}(1,d+1)$. Up to a compact subgroup, it can be fixed by fixing three points.
• Figure 2: In flat space and in AdS (left), when a region on a spatial slice, ${\cal R}$ is surrounded by its complement then $\overline{{\cal R}}$ extends to infinity. But in dS (right), every region ${\cal R}$ surrounds and is surrounded by its complement on a sphere.