Hyper non-Gaussianities in inflation with strongly non-geodesic motion
Published 2019-02-08Version 1
Several recent proposals to embed inflation into high-energy physics rely on inflationary dynamics characterized by a strongly non-geodesic motion in negatively curved field space. This naturally leads to a transient instability of perturbations on sub-Hubble scales, and to their exponential amplification. Supported by first-principle numerical computations, we demonstrate that a non-standard single-field effective field theory with imaginary speed of sound enables one to gain analytical insight into primordial non-Gaussianities in this type of models. We show that the bispectrum is enhanced in flattened configurations and, more importantly, that the trispectrum and all higher-order correlation functions are exponentially amplified. These "hyper non-Gaussianities", whose amplitude we can relate to the amplification of the tree-level power spectrum, can easily lead to a loss of perturbative control. For example our results exclude the recent proposal of hyperinflation in its most interesting incarnation that satisfies the de Sitter swampland conjecture. More generally we provide powerful model-independent constraints on non-standard inflationary attractors motivated by the search for ultraviolet completions of inflation.