Primordial Power Spectrum Reconstruction From CMB Weak Lensing Power Spectrum

TL;DR

This paper presents a novel method using a modified Richardson-Lucy deconvolution algorithm to reconstruct the primordial power spectrum from CMB weak lensing data, offering a cleaner and independent probe of early universe fluctuations.

Contribution

The work introduces a new reconstruction technique for the primordial power spectrum from weak lensing data, avoiding secondary effects present in temperature-based methods.

Findings

Reconstructed broad features of the primordial power spectrum over different k scales.

Demonstrated the effectiveness of the method using simulated Planck data and error analysis.

Provided an algorithm for optimal sampling of the primordial power spectrum based on data and errors.

Abstract

We use the modified Richardson-Lucy deconvolution algorithm to reconstruct the Primordial Power Spectrum from the Weak Lensing Power spectrum reconstructed from the CMB anisotropies. This provides an independent window to observe and constrain the PPS $P_R(k)$ along different $k$ scales as compared to CMB Temperature Power Spectrum. The Weak Lensing Power spectrum does not contain secondary variations in power and hence is cleaner, unlike the Temperature Power spectrum which suffers from lensing which is visible in its PPS reconstructions. We demonstrate that the physical behaviour of the weak lensing kernel is different from the temperature kernel and reconstructs broad features over $k$. We provide an in-depth analysis of the error propagation using simulated data and Monte-Carlo sampling, based on Planck best-fit cosmological parameters to simulate the data and cosmic variance limited error bars. The error and initial condition analysis provides a clear picture of the optimal reconstruction region for the estimator and we provide and algorithm for $P_R(k)$ sampling to be used based on the given data, errors and its binning properties. Eventually we plan to use this method on actual mission data and provide a cross reference to PPS reconstructed from other sectors and any possible features in them.