PRISM: Recovery of the primordial spectrum from Planck data.

Aims. 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. Methods. 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. Results. We applied PRISM to 100 simulated Planck data to investigate its performance on Planck-like data.We then applied PRISM to the Planck PR1 power spectrum to recover the primordial power spectrum.We also tested the algorithm's ability to recover a small localised feature at k ∼ 0:125 Mpc-1, which caused a large dip at ࡁ ∼ 1800 in the angular power spectrum. Conclusions. We find no significant departures from the fiducial Planck PR1 near scale-invariant primordial power spectrum with As = 2:215 x 10-9 and ns = 0:9624. [ABSTRACT FROM AUTHOR]