Nonlinear Excitations in Inflationary Power Spectra
  We develop methods to calculate the curvature power spectrum in models where
features in the inflaton potential nonlinearly excite modes and generate high
frequency features in the spectrum. The first nontrivial effect of excitations
generating further excitations arises at third order in deviations from slow
roll. If these further excitations are contemporaneous, the series can be
resummed, showing the exponential sensitivity of the curvature spectrum to
potential features. More generally, this exponential approximation provides a
power spectrum template which nonlinearly obeys relations between excitation
coefficients and whose parameters may be appropriately adjusted. For a large
sharp step in the potential, it greatly improves the analytic power spectrum
template and its dependence on potential parameters. For axionic oscillations
in the potential, it corrects the mapping between the potential and the
amplitude, phase and zero point of the curvature oscillations, which might
otherwise cause erroneous inferences in for example the tensor-scalar ratio,
formally even when that amplitude is $10^3$ times larger than the slow roll
power spectrum. It also estimates when terms that produce double frequency
oscillations that are usually omitted when analyzing data should be included.
These techniques should allow future studies of high frequency features in the
CMB and large scale structure to extend to higher amplitude and/or higher
precision.
