Concerning the statistics of cosmic magnetism

TL;DR

This paper analyzes the statistical properties of primordial magnetic fields and their impact on the CMB, extending previous studies with analytical results for various spectra and discussing implications for non-Gaussianity.

Contribution

It provides new analytical results for the stress statistics of primordial magnetic fields across different spectra, including non-power law cases, and discusses their effects on the CMB.

Findings

Confirmed and extended stress statistics at one- and two-point levels.

Derived analytical results for power-law spectra and specific non-power law cases.

Discussed potential impacts on CMB non-Gaussianity.

Abstract

Magnetic fields appear to be a generic feature of the early universe and are a natural source of secondary CMB non-Gaussianity. In recent years the statistical nature of the stresses of a primordial magnetic field has been well studied. In this paper we confirm and extend these studies at one- and two-point level, and present analytical results for a wide range of power-law spectra. We also consider two non-power law cases of interest: a blue spectrum with an extended damping tail on small scales, which could be generated by the non-linear mixing of density and vorticity; and a red spectrum with a damping tail on large scales. We then briefly consider the CMB impacts that result from such fields. While this paper focuses on the one- and two-point moments, the techniques we employ are designed to ease the analysis of the full bispectra induced by primordial magnetic fields.