### abstract

- Though simple inflationary models describe the CMB well, their corrections are often plagued by infrared effects that obstruct a reliable calculation of late-time behaviour. We adapt to cosmology tools designed to address similar issues in other physical systems with the goal of making reliable late-time inflationary predictions. The main such tool is Open EFTs which reduce in the inflationary case to Stochastic Inflation plus calculable corrections. We apply this to a simple inflationary model that is complicated enough to have dangerous IR behaviour yet simple enough to allow the inference of late-time behaviour. We find corrections to standard Stochastic Inflationary predictions for the noise and drift, and we find these corrections ensure the IR finiteness of both these quantities. The late-time probability distribution, ${\cal P}(\phi)$, for super-Hubble field fluctuations are obtained as functions of the noise and drift and so these too are IR finite. We compare our results to other methods (such as large-$N$ models) and find they agree when these models are reliable. In all cases we can explore in detail we find IR secular effects describe the slow accumulation of small perturbations to give a big effect: a significant distortion of the late-time probability distribution for the field. But the energy density associated with this is only of order $H^4$ at late times and so does {\em not} generate a dramatic gravitational back-reaction.