PRISM: Sparse recovery of the primordial power spectrum
Résumé
Aims. The primordial power spectrum describes the initial perturbations
in the Universe which eventually grew into the large-scale structure we observe today, and
thereby provides an indirect probe of inflation or other structure-formation mechanisms.
Here, we introduce a new method to estimate this spectrum from the empirical power
spectrum of cosmic microwave background maps. Methods. A sparsity-based linear inversion method, named PRISM, is
presented. This technique leverages a sparsity prior on features in the primordial power
spectrum in a wavelet basis to regularise the inverse problem. This non-parametric
approach does not assume a strong prior on the shape of the primordial power spectrum, yet
is able to correctly reconstruct its global shape as well as localised features. These
advantages make this method robust for detecting deviations from the currently favoured
scale-invariant spectrum. Results. We investigate the strength of this method on a set of WMAP
nine-year simulated data for three types of primordial power spectra: a near
scale-invariant spectrum, a spectrum with a small running of the spectral index, and a
spectrum with a localised feature. This technique proves that it can easily detect
deviations from a pure scale-invariant power spectrum and is suitable for distinguishing
between simple models of the inflation. We process the WMAP nine-year data and find no
significant departure from a near scale-invariant power spectrum with the spectral index
ns =
0.972. Conclusions. A high-resolution primordial power spectrum can be
reconstructed with this technique, where any strong local deviations or small global
deviations from a pure scale-invariant spectrum can easily be detected.
Origine : Publication financée par une institution
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