Lattice Monte Carlo of on Euclidean de Sitter
Angelo Caravano
We report the first Monte Carlo simulation of quantum field theory on Euclidean de Sitter space, . Rather than discretizing space, we use a spectral lattice based on spherical harmonics, keeping all symmetries exact at finite cutoff. For a massless theory, the zero-mode distribution reproduces the Starobinsky-Yokoyama equilibrium at weak coupling, and deviations closely follow the one-loop renormalization of . At strong bare coupling, the renormalized quartic coupling saturates near the ceiling of the one-loop renormalization-group flow. This saturation is the de Sitter counterpart of the triviality mechanism that bounds the Higgs mass in flat space. Our results confirm nonperturbatively that the infrared divergences of light scalars in de Sitter are correctly resummed by the stochastic formalism. More broadly, this work opens up de Sitter space to lattice Monte Carlo methods.