Cosmic Microwave Background Trispectrum and Primordial Magnetic Field Limits

TL;DR

This paper calculates the CMB trispectrum induced by primordial magnetic fields to set the most stringent limits yet on their strength, surpassing previous bispectrum and power spectrum constraints.

Contribution

It introduces a new measure of magnetic non-Gaussianity, the CMB trispectrum, and uses it to derive tighter constraints on primordial magnetic fields from WMAP data.

Findings

CMB trispectrum magnitude for magnetic energy density ~10^{-29}

CMB trispectrum magnitude for magnetic anisotropic stress ~10^{-19}

Upper limit on primordial magnetic field strength is around 1 nanogauss

Abstract

Primordial magnetic fields will generate non-Gaussian signals in the cosmic microwave background (CMB) as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. We compute a new measure of magnetic non-Gaussianity, the CMB trispectrum, on large angular scales, sourced via the Sachs-Wolfe effect. The trispectra induced by magnetic energy density and by magnetic scalar anisotropic stress are found to have typical magnitudes of approximately a few times 10^{-29} and 10^{-19}, respectively. Observational limits on CMB non-Gaussianity from WMAP data allow us to conservatively set upper limits of a nG, and plausibly sub-nG, on the present value of the primordial cosmic magnetic field. This represents the tightest limit so far on the strength of primordial magnetic fields, on Mpc scales, and is better than limits from the CMB bispectrum and all modes in the CMB power spectrum. Thus, the CMB trispectrum is a new and more sensitive probe of primordial magnetic fields on large scales.