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.
