Magnetic field evolution in cosmic filaments with LOFAR data

Measuring the magnetic field in cosmic filaments reveals how Universe is magnetised and process that it. Using Rotation Measures (RM) at 144-MHz from LoTSS DR2 data, we analyse rms of RM extragalactic component as a function redshift to investigate evolution with filaments. From previous results, find term dominated by contribution (more than 90 percent). Including an error account for minor local sources, fit data model physical filament field, evolving $B_f = B_{f,0}\,(1+z)^\alpha$ density drawn cosmological simulations five magnetogenesis scenarios. We best-fit slope range $\alpha [-0.2, 0.1]$ uncertainty $\sigma_\alpha 0.4$--0.5, which consistent no evolution. The comoving decreases $\gamma \alpha - 2 [-2.2, -1.9]$. mean strength $z=0$ $B_{f,0}=39$--84~nG. For typical gas overdensity $\delta_g=10$ $B_{f,0}^{10}=8$--26~nG. A primordial stochastic initial $B_{\rm Mpc} 0.04$--0.11~nG favoured. uniform rejected.