Constraining Primordial Magnetism

TL;DR

This paper investigates how primordial magnetic fields influence cosmic microwave background and matter power spectra, using cosmological data to set upper limits on their strength, with the tightest constraint being approximately 1.3 nanogauss.

Contribution

It introduces an approximate method to include non-linear magnetic effects in linear perturbation theory and constrains primordial magnetic field strength using multiple cosmological datasets.

Findings

Large-scale CMB data constrain magnetic fields to <6.4 nG.

Including SZ effect data tightens the limit to <4.1 nG.

Adding Lyman-alpha data further reduces the limit to ~1.3 nG.

Abstract

Primordial magnetic fields could provide an explanation for the galactic magnetic fields observed today, in which case they may also leave interesting signals in the CMB and the small-scale matter power spectrum. We discuss how to approximately calculate the important non-linear magnetic effects within the guise of linear perturbation theory, and calculate the matter and CMB power spectra including the SZ contribution. We then use various cosmological datasets to constrain the form of the magnetic field power spectrum. Using solely large-scale CMB data (WMAP7, QUaD and ACBAR) we find a 95% CL on the variance of the magnetic field at 1 Mpc of B_\lambda < 6.4 nG. When we include SPT data to constrain the SZ effect, we find a revised limit of B_\lambda < 4.1 nG. The addition of SDSS Lyman-alpha data lowers this limit even further, roughly constraining the magnetic field to B_\lambda < 1.3 nG.