The Knotted Sky II: Does BICEP2 require a nontrivial primordial power
  spectrum?
  An inflationary gravitational wave background consistent with BICEP2 is
difficult to reconcile with a simple power-law spectrum of primordial scalar
perturbations. Tensor modes contribute to the temperature anisotropies at
multipoles with $l\lesssim 100$, and this effect --- together with a prior on
the form of the scalar perturbations --- was the source of previous bounds on
the tensor-to-scalar ratio. We compute Bayesian evidence for combined fits to
BICEP2 and Planck for three nontrivial primordial spectra: a) a running
spectral index, b) a cutoff at fixed wavenumber, and c) a spectrum described by
a linear spline with a single internal knot. We find no evidence for a cutoff,
weak evidence for a running index, and significant evidence for a "broken"
spectrum. Taken at face-value, the BICEP2 results require two new inflationary
parameters in order to describe both the broken scale invariance in the
perturbation spectrum and the observed tensor-to-scalar ratio. Alternatively,
this tension may be resolved by additional data and more detailed analyses.
