Evolution of f_NL to the adiabatic limit

We study inflationary perturbations in multiple-field models, for which ζ typically evolves until all isocurvature modes decay — the “adiabatic limit”. We use numerical methods to explore the sensitivity of the local-shape bispectrum to the process by which this limit is achieved, finding an appreciable dependence on model-specific data such as the time at which slow-roll breaks down or the timescale of reheating. In models with a sum-separable potential where the isocurvature modes decay before the end of the slow-roll phase we give an analytic criterion for the asymptotic value of f_NL to be large. Other examples can be constructed using a waterfall field to terminate inflation while f_NL is transiently large, caused by descent from a ridge or convergence into a valley. We show that these two types of evolution are distinguished by the sign of the bispectrum, and give approximate expressions for the peak f_NL.