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We report a novel prediction from single-field inflation that even a tinystep in the inflaton potential can change our perception of primordialnon-Gaussianities of the curvature perturbation. Our analysis focuses on thetail of probability distribution generated by an upward step transition betweentwo stages of slow-roll evolution. The nontrivial background dynamics withoff-attractor behavior is identified. By using a non-perturbative $\delta N$analysis, we explicitly show that a highly non-Gaussian tail can be generatedby a tiny upward step, even when the conventional nonlinearity parameters$f_{NL}$, $g_{NL}$, etc. remain small. With this example, we demonstrate forthe first time the sensitive dependence of non-perturbative effects on the tailof probability distribution. Our scenario has an inconceivable application toprimordial black holes by either significantly boosting their abundance orcompletely forbidding their appearance.

One Small Step for an Inflaton, One Giant Leap for Inflation: a novel non-Gaussian tail and primordial black holes