Filaments’ RRM_f rms as a function of the redshift of the cosmological models used in this work. The RRMs are computed using the gas densities and magnetic fields from the MHD cosmological simulations (astroph and astroph 2 are the first and second astrophysical models discussed in Sect. 3). The error bars of the simulated LOS are reported, albeit smaller than the markers (the typical mean fractional error is 0.07 percent). The measured RRM rms is also shown for comparison, with the A_rrm/(1 + z) (left panel) or A_rrm/(1 + z)³ (right panel) term subtracted off to only display the filament component. The corresponding filament component of the best fit is also shown (red, thick, dashed line) along with its uncertainty (shaded area).