We present the first cosmological simulations of primordial magnetic fields derived from the constraints by the Cosmic Microwave Background observations, based on the fields gravitational effect on cosmological perturbations. We evolved different primordial magnetic field models with the {enzo} code and compared their observable signatures (and relative differences) in galaxy clusters, filaments and voids. The differences in synchrotron radio powers and Faraday Rotation measure from galaxy clusters are generally too small to be detected, whereas differences present in filaments will be testable with the higher sensitivity of the Square Kilometre Array. However, several statistical full-sky analyses, such as the cross-correlation between galaxies and diffuse synchrotron power, the Faraday Rotation structure functions from background radio galaxies, or the analysis of arrival direction of Ultra-High-Energy Cosmic Rays, can already be used to constrain these primordial field models.
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