True cosmic microwave background power spectrum estimation

P. Paykari¹, J.-L. Starck¹ and M. J. Fadili²

¹ Laboratoire AIM, UMR CEA-CNRS-Paris 7, Irfu, SAp/SEDI, Service d’Astrophysique, CEA Saclay, 91191 Gif-Sur-Yvette Cedex, France
e-mail: paniez.paykari@cea.fr
² GREYC CNRS UMR 6072, ENSICAEN, 6 Bd. du Maréchal Juin, 14050 Caen Cedex, France

Received: 5 October 2011
Accepted: 19 February 2012

Abstract

Aims. The cosmic microwave background (CMB) power spectrum is a powerful cosmological probe as it entails almost the entire statistical information of 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. We aim to recover the true underlying CMB power spectrum from the one realization that we have without knowing the cosmological parameters.

Methods. 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 very few coefficients in these two dictionaries and hence is very compressible.

Results. We studied the performance of these dictionaries in smoothing a set of simulated power spectra. Based on this, we developed a technique that estimates the true underlying CMB power spectrum from data, i.e., without a need to know the cosmological parameters.

Conclusions. This smooth estimated spectrum can be used to simulate CMB maps with similar properties as the true CMB simulations with the correct cosmological parameters. This allows us to perform 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.