A microscopic realization of dS$_3$

TL;DR

This paper proposes a duality between 2+1 dimensional pure de Sitter quantum gravity and a double-scaled matrix integral, linking cosmological correlators, string amplitudes, and horizon entropy in a novel framework.

Contribution

It introduces a precise duality between de Sitter quantum gravity and a matrix integral, connecting cosmological observables with matrix model resolvents and entropy counting.

Findings

Derived a quantum state of the universe at future infinity.

Connected cosmological correlators with complex Liouville string amplitudes.

Reproduced Gibbons-Hawking entropy through matrix entries counting.

Abstract

We propose a precise duality between pure de Sitter quantum gravity in 2+1 dimensions and a double-scaled matrix integral. This duality unfolds in two distinct aspects. First, by carefully quantizing the gravitational phase space, we arrive at a novel proposal for the quantum state of the universe at future infinity. We compute cosmological correlators of massive particles in the universe specified by this wavefunction. Integrating these correlators over the metric at future infinity yields gauge-invariant observables, which are identified with the string amplitudes of the complex Liouville string arXiv:2409.17246. This establishes a direct connection between integrated cosmological correlators and the resolvents of the matrix integral dual to the complex Liouville string, thereby demonstrating one aspect of the dS$_3$/matrix integral duality. The second aspect concerns the cosmological horizon of the dS static patch and the Gibbons-Hawking entropy it is conjectured to encode. We show that this entropy can be reproduced exactly by counting the entries of the matrix.