Reconstruction of the Primordial Power Spectrum by Direct Inversion

TL;DR

This paper presents a novel direct inversion method using SVD to reconstruct the primordial power spectrum from CMB data, reducing degeneracies and enabling detailed analysis within MCMC frameworks.

Contribution

The paper introduces a new SVD-based inversion technique for $P(k)$ reconstruction from CMB observations, improving upon previous methods by reducing degeneracies.

Findings

Best-fit primordial power spectrum obtained

Method integrated with MCMC for joint parameter estimation

Enhanced resolution of $P(k)$ features

Abstract

We introduce a new method for reconstructing the primordial power spectrum, $P(k)$, directly from observations of the Cosmic Microwave Background (CMB). We employ Singular Value Decomposition (SVD) to invert the radiation perturbation transfer function. The degeneracy of the multipole $\ell$ to wavenumber $k$ linear mapping is thus reduced. This enables the inversion to be carried out at each point along a Monte Carlo Markov Chain (MCMC) exploration of the combined $P(k)$ and cosmological parameter space. We present best--fit $P(k)$ obtained with this method along with other cosmological parameters.