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Several recent proposals to embed inflation into high-energy physics rely oninflationary dynamics characterized by a strongly non-geodesic motion innegatively curved field space. This naturally leads to a transient instabilityof perturbations on sub-Hubble scales, and to their exponential amplification.Supported by first-principle numerical computations, and by the analyticalinsight provided by the effective field theory of inflation, we show that thebispectrum is enhanced in flattened configurations, and we argue that ananalogous result holds for all higher-order correlation functions. These``hyper non-Gaussianities'' thus provide powerful model-independent constraintson non-standard inflationary attractors motivated by the search for ultravioletcompletions of inflation.

Hyper non-Gaussianities in inflation with strongly non-geodesic motion