PRISM: Recovery of the primordial spectrum from Planck data

Abstract

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 $A_s=2.215\times 10^{-9}$ and $n_s=0.9624$.

arXiv comment4 pages, 2 figures, Accepted in A&A; Updated to match the final accepted version

References in corpus (9)

• BICEP2 I: Detection Of B-mode Polarization at Degree Angular Scales
• Planck 2013 results. XXII. Constraints on inflation
• MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
• Constraints on Cosmology from the Cosmic Microwave Background Power Spectrum of the 2500 ${\mathrm{deg}}^2$ SPT-SZ Survey
• Search for TeV Gamma-ray Emission from GRB 100621A, an extremely bright GRB in X-rays, with H.E.S.S
• BICEP2 II: Experiment and Three-Year Data Set
• Joint Planck and WMAP CMB Map Reconstruction
• Ruling out the power-law form of the scalar primordial spectrum
• PRISM: Sparse Recovery of the Primordial Power Spectrum

Cited by in corpus (6)

• Search for features in the spectrum of primordial perturbations using Planck and other datasets
• CMB reconstruction from the WMAP and Planck PR2 data
• Joint Planck and WMAP Assessment of Low CMB Multipoles
• Scale-invariant scalar spectrum from the nonminimal derivative coupling with fourth-order term
• Constraining the primordial power spectrum using a differentiable likelihood
• Polarized CMB recovery with sparse component separation