CMB bispectrum from primordial magnetic fields on large angular scales

TL;DR

This paper investigates how primordial magnetic fields induce non-Gaussian signals in the CMB, specifically through the bispectrum on large scales, providing a new method to constrain magnetic field strength.

Contribution

It calculates the CMB bispectrum caused by primordial magnetic fields on large angular scales, offering a novel observational probe of these fields.

Findings

Estimated bispectrum value for B_0 ~ 3 nG is ~10^{-22}

Current limits constrain magnetic fields to B_0 < 35 nG

Method can be refined with additional magnetically induced bispectrum contributions

Abstract

Primordial magnetic fields lead to non-Gaussian signals in the Cosmic Microwave Background (CMB) even at the lowest order, as magnetic stresses, and the temperature anisotropy they induce, depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arise only as a higher order effect. We propose here a novel probe of stochastic primordial magnetic fields that exploits the characteristic CMB non-Gaussianity that they induce. In particular, we compute the CMB bispectrum ($b_{l_{_1}l_{_2}l_{_3}}$) induced by stochastic primordial fields on large angular scales. We find a typical value of $l_1(l_1+1)l_3(l_3+1) b_{l_{_1}l_{_2}l_{_3}} \sim 10^{-22}$, for magnetic fields of strength $B_0 \sim 3$ nano Gauss and with a nearly scale invariant magnetic spectrum. Current observational limits on the bispectrum allow us to set upper limits on $B_0 \sim 35$ nano Gauss, which can be improved by including other magnetically induced contributions to the bispectrum.