Using cosmological MHD simulations of the magnetic field in galaxy clusters and filaments we evaluate the possibility to infer the magnetic field strength in filaments by measuring cross-correlation functions between Faraday Rotation Measures (RM) and the galaxy density field. We also test the reliability of recent estimates considering the problem of data quality and Galactic foreground (GF) removal in current datasets. Besides the two self-consistent simulations of cosmological magnetic fields based on primordial seed fields and galactic outflows analyzed here, we also explore a larger range of models scaling up the resulting magnetic fields of one of the simulations. We find that, if an unnormalized estimator for the cross-correlation functions and a GF removal procedure is used, the detectability of the cosmological signal is only possible for future instruments (e.g. SKA and ASKAP). However, mapping of the observed RM signal to the underlying magnetization of the Universe (both in space and time) is an extremely challenging task which is limited by the ambiguities of our model parameters, as well as to the weak response of the RM signal in low density environments. Therefore, we conclude that current data cannot constrain the amplitude and distribution of magnetic fields within the large scale structure and a detailed theoretical understanding of the build up and distribution of magnetic fields within the Universe will be needed for the interpretation of future observations.
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