PRISM: Recovery of the primordial spectrum from Planck data

The primordial power spectrum describes the initial perturbations that seeded the large-scale structure we observe today. It provides an indirect probe of inflation or other structure-formation mechanisms. In this letter, we recover the primordial power spectrum from the Planck PR1 dataset, using our recently published algorithm PRISM. PRISM is a sparsity-based inversion method, that aims at recovering features in the primordial power spectrum from the empirical power spectrum of the cosmic microwave background (CMB). This ill-posed inverse problem is regularised using a sparsity prior on features in the primordial power spectrum in a wavelet dictionary. Although this non-parametric method does not assume a strong prior on the shape of the primordial power spectrum, it is able to recover both its general shape and localised features. As a results, this approach presents a reliable way of detecting deviations from the currently favoured scale-invariant spectrum. We applied PRISM to 100 simulated Planck data to investigate its performance on Planck-like data. We also tested the algorithm's ability to recover a small localised feature at $k \sim 0.125$ Mpc$^{-1}$, which caused a large dip at $\ell \sim 1800$ in the angular power spectrum. We then applied PRISM to the Planck PR1 power spectrum to recover the primordial power spectrum. We find no significant departures from the fiducial Planck PR1 near scale-invariant primordial power spectrum with $A_s=2.215\times10^{-9}$ and $n_s = 0.9624$.