Simulated Rotation Measure Sky from Primordial Magnetic Fields
Primordial Magnetic Fields (PMFs) -- magnetic fields originating in the early Universe and permeating the cosmological scales today -- can explain the observed microGauss-level magnetisation of galaxies and their clusters. In light of current and upcoming all-sky radio surveys, PMFs have drawn attention not only as major candidates for explaining the large-scale magnetisation of the Universe, but also as potential probes of early-Universe physics. In this paper, using cosmological simulations coupled with light-cone analysis, we study for the first time the imprints of the PMF structure on the mean rotation measure (RM) originating in the intergalactic medium (IGM), $\langle \mathrm{RM_{IGM}}\rangle$. We introduce a new method for producing full-sky $\mathrm{RM_{IGM}}$ distributions and analyse the autocorrelation of $\mathrm{RM_{IGM}}$ on small and large angular scales; we find that PMF structures indeed show distinct signatures. The large-scale uniform model (characterised by an initially unlimited coherence scale) leads to correlations up to 90 degrees, while correlations for small-scale stochastic PMF models drop by factor of $100$ at $ 0.17, 0.13$ and 0.11 degrees angular scales, corresponding to $5.24, 4.03$ and $3.52$ Mpc scales (at $z=2$ redshift) for magnetic fields with comoving $3.49, 1.81, 1.00 $ Mpc/h coherence scales, respectively; the correlation amplitude of the PMF model with comoving $\sim 19$ Mpc/h coherence scale drops only by factor of $10$ at 1 degree (30.6 Mpc). These results suggests that improvements in the modelling of Galactic RM will be necessary to investigate the signature of large-scale correlated PMFs. A comparison of $\langle \mathrm{RM_{IGM}}\rangle$ redshift dependence obtained from our simulations with that from the LOFAR Two-metre Sky Survey shows agreement with our previous upper limits' estimates on the PMF strength derived from RM-rms analysis.