Light scalars in de Sitter: the stochastic story
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.