Description
Light, polynomially self-interacting scalars in de Sitter notoriously generate infrared (IR) divergences: on superhorizon scales, their fluctuations grow so large that perturbation theory breaks down. We address this problem using non-perturbative techniques from stochastic inflation, by encoding the superhorizon dynamics in a probability distribution involving composite operators of the light scalar. We find that these composites behave as late-time conformal primaries, with their position-space four-point function collapsing to a strikingly simple power law. We conjecture a new physical picture: light interacting scalars in de Sitter effectively hadronize on superhorizon scales, producing a tower of composite states. We then explore whether this emergent spectrum can be captured within a weakly coupled effective field theory, which would amount to recasting the stochastic scalar IR-dynamics in terms of new, effective degrees of freedom.
