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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 ℓ ~ 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 × 10-9 and ns = 0.9624.


Lanusse, F.; Paykari, P.; Starck, J.-L.; Sureau, F.; Bobin, J.; Rassat, A.


Astronomy & Astrophysics

Paper Publication Date

November 2014

Paper Type


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