PRISM: Sparse Recovery of the Primordial Power Spectrum

Abstract

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 (CMB) maps. A sparsity-based linear inversion method, coined \textbf{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. We investigate the strength of this method on a set of WMAP 9-year simulated data for three types of primordial power spectra: a nearly scale-invariant spectrum, a spectrum with a small running of the spectral index, and a spectrum with a localised feature. This technique proves to 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 9-year data and find no significant departure from a nearly scale-invariant power spectrum with the spectral index $n_s=0.972$. 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.

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Cited by in corpus (14)

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• High Resolution Weak Lensing Mass-Mapping Combining Shear and Flexion
• Search for features in the spectrum of primordial perturbations using Planck and other datasets
• Exploring the spectroscopic diversity of type Ia supernovae with DRACULA: a machine learning approach
• Using wavelets to capture deviations from smoothness in galaxy-scale strong lenses
• Sparse Bayesian mass-mapping with uncertainties: local credible intervals
• Primordial Power Spectrum features and $f_{NL}$ constraints
• PRISM: Recovery of the primordial spectrum from Planck data
• Reconstructing the EFT of Inflation from Cosmological Data
• Spectral Distortion Signatures of Step-like Inflationary Potential
• All-sky reconstruction of the primordial scalar potential from WMAP temperature data
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• J-PAS: forecast on the primordial power spectrum reconstruction