A Consistency Relation for Single-Field Inflation with Power Spectrum
  Oscillations
  We derive a theoretical upper bound on the oscillation frequency in the
scalar perturbation power spectrum of single-field inflation. Oscillations are
most naturally produced by modified vacua with varying phase. When this phase
changes rapidly, it induces strong interactions between the scalar
fluctuations. If the interactions are sufficiently strong the theory cannot be
evaluated using perturbation theory, hence imposing a limit on the oscillation
frequency. This complements the bound found by Weinberg governing the validity
of effective field theory. The generalized consistency relation also allows one
to use squeezed configurations of higher-point correlations to place
constraints on the power spectrum oscillations.
