Intergalactic medium rotation measure of primordial magnetic fields

The Faraday rotation effect, quantified by the Rotation Measure (RM), is a powerful probe of the large-scale magnetization of the Universe - tracing magnetic fields not only on galaxy and galaxy cluster scales but also in the intergalactic Medium (IGM; referred to as RM₈₆₌). The redshift dependence of the latter has extensively been explored with observations. It has also been shown that this relation can help to distinguish between different large-scale magnetization scenarios. We study the evolution of this RM₈₆₌ for different primordial magnetogenesis scenarios to search for the imprints of primordial magnetic fields (PMFs; magnetic fields originating in the early Universe) on the redshift-dependence of RM₈₆₌. We use cosmological magnetohydrodynamic (MHD) simulations for evolving PMFs during large-scale structure formation, coupled to the light cone analysis to produce a realistic statistical sample of mock RM₈₆₌ images. We study the predicted behavior for the cosmic evolution of RM₈₆₌ for different correlation lengths of PMFs, and provide fitting functions for their dependence on redshifts. We compare these mock RM trends with the recent analysis of the the LOw-Frequency ARray (LOFAR) RM Grid and find that large-scale-correlated PMFs should have (comoving) strengths 0. 75 nanoGauss, if originated during inflation with the scale invariant spectrum and (comoving) correlation length 19 cMpc/h or 30 nanoGauss if they originated during phase-transition epochs with the comoving correlation length 1 cMpc/h. Our findings agree with previous observations and confirm the results of semi-analytical studies, showing that upper limits on the PMF strength decrease as their coherence scales increase.