Random Euclidean CFT$_2$ from Triangulated dS$_3$ Gravity

Abstract

We propose a random Euclidean CFT description of three-dimensional de Sitter gravity, with fixed central charge and primary spectrum but fluctuating operator product coefficients. Our construction starts from compact regions assembled from generalized hyperbolic tetrahedra. We analytically continue the gravitational amplitudes computed from these triangulations to de Sitter parameters and use them to infer OPE correlations. We recover matching normalized amplitudes from a complex Liouville cosmological wavefunction. A non-Gaussian fourth moment encodes the hyperbolic core volume in an oscillatory semiclassical phase. We construct the associated Lorentzian de Sitter spacetime and show that derivatives of this phase recover its boost holonomies. Its spacelike future boundary carries a positive-definite conformal metric, while the wavefunction obeys Euclidean conformal Ward identities. These relations connect the proposed OPE statistics to both the Euclidean boundary description and the Lorentzian bulk geometry. Integrating the absolute square of the cosmological wavefunction over boundary moduli gives cosmological observables. Their long-collar factorization reproduces the edge measure of the two-matrix model.