PRISM: Sparse recovery of the primordial spectrum from WMAP9 and Planck datasets

Abstract

Abstract. The primordial power spectrum is an indirect probe of inflation or other structureformation mechanisms. We introduce a new method, named PRISM, to estimate this spectrum from the empirical cosmic microwave background (CMB) power spectrum. This is a sparsitybased inversion method, which leverages a sparsity prior on features in the primordial spectrum in a wavelet dictionary to regularise the inverse problem. This non-parametric approach is able to reconstruct the global shape as well as localised features of the primordial spectrum accurately and proves to be robust for detecting deviations from the currently favoured scale-invariant spectrum. We investigate the strength of this method on a set of WMAP nine-year simulated data for three types of primordial spectra and then process the WMAP nine-year data as well as the Planck PR1 data. We find no significant departures from a near scale-invariant spectrum.

Primordial Power Spectrum reconstruction from CMB Weak Lensing Power Spectrum

“…This is by no means the last word as many other parametrizations exist, from light adjustments like a k dependent n s (running the power law), to specific model dependent features in the PPS like steps and valleys [25,26]. Given the large and diverse range of inflation models, there is a well established framework that seeks to reconstruct the PPS using a model independent approach [5,[39][40][41][42]. Much work has been done on this approach, using the Richardson-Lucy deconvolution algorithm [1,3,4,7,10,14].…”

Primordial Power Spectrum from Lensed CMB Temperature Spectrum using Iterative Delensing

“…Recent work has focussed on analyzing the the H 0 tension in context of a free-form P R (k) reconstruction using the improved Richardson-Lucy (IRL) deconvolution algorithm [6,17] as well as for general feature hunting. There are also other free-form and other reconstruction methods that have been developed [11,[36][37][38][39][40]43]. Results have shown promise within the bounds and assumptions of this method, and produce a relatively high frequency (with respect to the reconstruction bounds) oscillatory feature at high k regions, while considering a prior assumption of the H 0 , Ω m and σ 8 evaluated from local Universe observations and remaining parameters from ΛCDM inference.…”