Numerical stochastic inflation constrained by frozen noise

Stochastic inflation can resolve strong inflationary perturbations, which seed primordial black holes. I present a fast , accurate way to compute these perturbations in typical black hole producing single-field models, treating the short-wavelength Fourier modes beyond the de Sitter approximation. The squeezing and freezing of the modes reduces the problem to one dimension , the resulting new form of the stochastic equations, dubbed `constrained stochastic inflation,' can be solved efficiently with semi-analytical techniques and numerical importance sampling. In an example case, the perturbation distribution is resolved in seconds deep into its non-Gaussian tail, a speed-up of factor 109 compared to a previous study. Along the way, I comment on the role of the momentum constraint in stochastic inflation.