Perturbative Unitarity of Inflationary Models with Features

We consider the pertubative consistency of inflationary models with features with effective field theory methods. By estimating the size of one-loop contributions to the three-point function, we find the energy scale where their contribution is of the same order of the tree-level amplitude. It is well-known that beyond that scale, perturbative unitarity is lost and the theory is no more under theoretical control. Requiring that all the relevant energy scales of the problem are below this cutoff, we derive a strong upper bound on the sharpness of the feature, or equivalently on its characteristic time scale, which is independent on the amplitude of the feature itself. We point out that the sharp features which seem to provide better fits to the CMB power spectrum are already outside this bound, questioning the consistency of the models that predict them.