Holographic Map for Cosmological Horizons

TL;DR

This paper introduces a holographic framework linking Einstein gravity in de Sitter space with a spin-based quantum mechanical model, capturing chaotic and perturbative aspects of quantum gravity.

Contribution

It presents a novel holographic map connecting gravitational dynamics to a spin system, incorporating non-local chaos and local perturbative spectra.

Findings

Holographic map between gravity and spin system established

Chaotic dynamics generated by non-local Hamiltonian component

Perturbative bulk spectrum recovered from local Hamiltonian part

Abstract

We propose a holographic map between Einstein gravity coupled to matter in a de Sitter background and large N quantum mechanics of a system of spins. Holography maps a spin model with a finite dimensional Hilbert space defined on a version of the stretched horizon into bulk gravitational dynamics. The full Hamiltonian of the spin model contains a non-local piece which generates chaotic dynamics, widely conjectured to be a necessary part of quantum gravity, and a local piece which recovers the perturbative spectrum in the bulk.