The Knotted Sky I: Planck constraints on the primordial power spectrum
  Using the temperature data from Planck we search for departures from a
power-law primordial power spectrum, employing Bayesian model-selection and
posterior probabilities. We parametrize the spectrum with $n$ knots located at
arbitrary values of $\log{k}$, with both linear and cubic splines. This
formulation recovers both slow modulations and sharp transitions in the
primordial spectrum. The power spectrum is well-fit by a featureless, power-law
at wavenumbers $k>10^{-3} \, \mathrm{Mpc}^{-1}$. A modulated primordial
spectrum yields a better fit relative to $\Lambda$CDM at large scales, but
there is no strong evidence for a departure from a power-law spectrum.
Moreover, using simulated maps we show that a local feature at $k \sim 10^{-3}
\, \mathrm{Mpc}^{-1}$ can mimic the suppression of large-scale power. With
multi-knot spectra we see only small changes in the posterior distributions for
the other free parameters in the standard $\Lambda$CDM universe. Lastly, we
investigate whether the hemispherical power asymmetry is explained by
independent features in the primordial power spectrum in each ecliptic
hemisphere, but find no significant differences between them.
