True CMB Power Spectrum Estimation

TL;DR

This paper introduces a novel method to recover the true CMB power spectrum from a single observed realization using sparse representations, enabling accurate simulations without prior knowledge of cosmological parameters.

Contribution

It develops a new technique leveraging sparsity in DCT and Wavelet dictionaries to estimate the true CMB power spectrum independently of cosmological parameters.

Findings

CMB power spectrum is highly compressible in DCT and Wavelet dictionaries.

The method accurately recovers the true spectrum from simulated data.

The approach enables parameter-free Monte Carlo simulations of CMB maps.

Abstract

The cosmic microwave background (CMB) power spectrum is a powerful cosmological probe as it entails almost all the statistical information of the CMB perturbations. Having access to only one sky, the CMB power spectrum measured by our experiments is only a realization of the true underlying angular power spectrum. In this paper we aim to recover the true underlying CMB power spectrum from the one realization that we have without a need to know the cosmological parameters. The sparsity of the CMB power spectrum is first investigated in two dictionaries; Discrete Cosine Transform (DCT) and Wavelet Transform (WT). The CMB power spectrum can be recovered with only a few percentage of the coefficients in both of these dictionaries and hence is very compressible in these dictionaries. We study the performance of these dictionaries in smoothing a set of simulated power spectra. Based on this, we develop a technique that estimates the true underlying CMB power spectrum from data, i.e. without a need to know the cosmological parameters. This smooth estimated spectrum can be used to simulate CMB maps with similar properties to the true CMB simulations with the correct cosmological parameters. This allows us to make Monte Carlo simulations in a given project, without having to know the cosmological parameters. The developed IDL code, TOUSI, for Theoretical pOwer spectrUm using Sparse estImation, will be released with the next version of ISAP.