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We perform uniformly sampled large-scale cosmological simulations includingmagnetic fields with the moving mesh code AREPO. We run two sets of MHDsimulations: one including adiabatic gas physics only; the other featuring thefiducial feedback model of the Illustris simulation. In the adiabatic case, themagnetic field amplification follows the $B \propto \rho^{2/3}$ scaling derivedfrom `flux-freezing' arguments, with the seed field strength providing anoverall normalization factor. At high baryon overdensities the amplification isenhanced by shear flows and turbulence. Feedback physics and the inclusion ofradiative cooling change this picture dramatically. In haloes, gas collapses tomuch larger densities and the magnetic field is amplified strongly and to thesame maximum intensity irrespective of the initial seed field of which anymemory is lost. At lower densities a dependence on the seed field strength andorientation, which in principle can be used to constrain models of cosmicmagnetogenesis, is still present. Inside the most massive haloes magneticfields reach values of $\sim 10-100\,\,{\rm \mu G}$, in agreement with galaxycluster observations. The topology of the field is tangled and gives rise torotation measure signals in reasonable agreement with the observations.However, the rotation measure signal declines too rapidly towards larger radiias compared to observational data.

The large-scale properties of simulated cosmological magnetic fields