Probing Primordial Magnetism with Off-Diagonal Correlators of CMB Polarization

TL;DR

This paper explores how primordial magnetic fields can be detected through their effects on CMB polarization, especially via Faraday rotation, and evaluates the potential of current and future experiments to measure these fields.

Contribution

It provides a comprehensive analysis of the detectability of primordial magnetic fields using off-diagonal correlators of CMB polarization, accounting for lensing contamination and multi-frequency observations.

Findings

Planck-like experiments can detect nG scale-invariant PMF at 90GHz.

Future experiments could detect magnetic fields as weak as 10^{-10} G.

Multi-frequency observations enhance detection prospects.

Abstract

Primordial magnetic fields (PMF) can create polarization $B$-modes in the cosmic microwave background (CMB) through Faraday rotation (FR), leading to non-trivial 2-point and 4-point correlators of the CMB temperature and polarization. We discuss the detectability of primordial magnetic fields using different correlators and evaluate their relative merits. We have fully accounted for the contamination by weak lensing, which contributes to the variance, but whose contribution to the 4-point correlations is orthogonal to that of FR. We show that a Planck-like experiment can detect scale-invariant PMF of nG strength using the FR diagnostic at 90GHz, while realistic future experiments at the same frequency can detect 10^{-10} G. Utilizing multiple frequencies will improve on these prospects, making FR of CMB a powerful probe of scale-invariant PMF.