Stringent Limit on Primordial Magnetic Fields from the Cosmic Microwave Background Radiation

TL;DR

This paper sets new, more stringent upper limits on primordial magnetic fields by analyzing their effects on cosmic microwave background anisotropies using advanced numerical simulations and observational data.

Contribution

It introduces a novel analysis incorporating inhomogeneous recombination effects to derive tighter constraints on primordial magnetic fields from CMB data.

Findings

Total magnetic field strength cannot exceed 47 pG for scale-invariant spectra.

Limits are 8.9 pG for violet Batchelor spectrum.

Constraints are over an order of magnitude more stringent than previous bounds.

Abstract

Primordial magnetic fields (PMFs), being present before the epoch of cosmic recombination, induce small-scale baryonic density fluctuations. These inhomogeneities lead to an inhomogeneous recombination process that alters the peaks and heights of the large-scale anisotropies of the cosmic microwave backround (CMB) radiation. Utilizing numerical compressible MHD calculations and a Monte Carlo Markov chain analysis, which compares calculated CMB anisotropies with those observed by the \textit{WMAP} and \textit{Planck} satellites, we derive limits on the magnitude of putative PMFs. We find that the {\it total} remaining present day field, integrated over all scales, cannot exceed 47 pG for scale-invariant PMFs and 8.9 pG for PMFs with a violet Batchelor spectrum at 95\% confidence level. These limits are more than one order of magnitude more stringent than any prior stated limits on PMFs from the CMB which have not accounted for this effect.