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We use the CRPropa code to simulate the propagation of ultra high energycosmic rays (with energy $\geq 10^{18} \rm eV$ and pure proton composition)through extragalactic magnetic fields that have been simulated with thecosmological ENZO code.We test both primordial and astrophysical magnetogenesisscenarios in order to investigate the impact of different magnetic fieldstrengths in clusters, filaments and voids on the deflection of cosmic rayspropagating across cosmological distances. We also study the effect ofdifferent source distributions of cosmic rays around simulated Milky-Way likeobservers. Our analysis shows that the arrival spectra and anisotropy of eventsare rather insensitive to the distribution of extragalactic magnetic fields,while they are more affected by the clustering of sources within a $\sim 50$Mpc distance to observers. Finally, we find that in order to reproduce theobserved degree of isotropy of cosmic rays at $\sim $ EeV energies, the averagemagnetic fields in cosmic voids must be $\sim 0.1 \rm \ nG$, providing limitson the strength of primordial seed fields.

Propagation of Ultra High Energy Cosmic Rays in Extragalactic Magnetic Fields: A view from cosmological simulations