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 $\mathrm{RM}_{\text{IGM}}$). 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 $\mathrm{RM}_{\text{IGM}}$ 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 $\mathrm{RM}_{\text{IGM}}$. 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 $\mathrm{RM}_{\text{IGM}}$ images. We study the predicted behavior for the cosmic evolution of $\mathrm{RM}_{\text{IGM}}$ 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 $\lesssim 0.75$ nanoGauss, if originated during inflation with the scale invariant spectrum and (comoving) correlation length $\sim 19$ cMpc/h or $ \lesssim 30$ nanoGauss if they originated during phase-transition epochs with the comoving correlation length $\sim 1$ 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.