Using the temperature data from Planck we search for departures from apower-law primordial power spectrum, employing Bayesian model-selection andposterior probabilities. We parametrize the spectrum with $n$ knots located atarbitrary values of $\log{k}$, with both linear and cubic splines. Thisformulation recovers both slow modulations and sharp transitions in theprimordial spectrum. The power spectrum is well-fit by a featureless, power-lawat wavenumbers $k>10^{-3} \, \mathrm{Mpc}^{-1}$. A modulated primordialspectrum yields a better fit relative to $\Lambda$CDM at large scales, butthere 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. Withmulti-knot spectra we see only small changes in the posterior distributions forthe other free parameters in the standard $\Lambda$CDM universe. Lastly, weinvestigate whether the hemispherical power asymmetry is explained byindependent features in the primordial power spectrum in each ecliptichemisphere, but find no significant differences between them.
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