  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.
