Free scalar correlators in de Sitter via the stochastic approach beyond slow roll.

The stochastic approach to calculating scalar correlation functions in de Sitter spacetime is extended beyond the overdamped ``slow roll'' approximation. We find that the stochastic noise evaluated by the Starobinsky-Yokoyama approach, extended to beyond the overdamped limit, does not reproduce the exact asymptotic long-distance behaviour of field correlators in free field theory. Therefore we propose a new method whereby the stochastic 2-point function $\langle\phi(t,\mathbf{x})\phi(t',\mathbf{x}')\rangle$ is matched to its QFT counterpart in order to calculate the correct noise. Using this matched noise, we proceed to show that the stochastic approach correctly reproduces all higher-order correlators for free fields.