  We study the CMB observables in axion monodromy inflation. These
well-motivated scenarios for inflation in string theory have monomial
potentials over super-Planckian field ranges, with superimposed sinusoidal
modulations from instanton effects. Such periodic modulations of the potential
can drive resonant enhancements of the correlation functions of cosmological
perturbations, with characteristic modulations of the amplitude as a function
of wavenumber. We give an analytical result for the scalar power spectrum in
this class of models, and we determine the limits that present data places on
the amplitude and frequency of modulations. Then, incorporating an improved
understanding of the realization of axion monodromy inflation in string theory,
we perform a careful study of microphysical constraints in this scenario. We
find that detectable modulations of the scalar power spectrum are commonplace
in well-controlled examples, while resonant contributions to the bispectrum are
undetectable in some classes of examples and detectable in others. We conclude
that resonant contributions to the spectrum and bispectrum are a characteristic
signature of axion monodromy inflation that, in favorable cases, could be
detected in near-future experiments.
