The Intergalactic Medium (IGM) is the region comprising the environment between the galaxies. Gamma-ray observations have provided lower limits to IGM magnetic fields of the order of ≳10–16 G. Magnetic fields are continuously ejected from galaxies by jets and galactic winds. However, the origin and evolution of cosmic magnetic fields in the more diffuse regions, like voids, is still debated. The difficulties in directly measuring magnetic fields and their coherent scales, make hydrodynamic and magnetohydrodynamic (MHD) cosmological simulations useful tools to shed light on this debate. As a first approach, we have performed hydrodynamic cosmological simulations assuming energy equipartition as an initial condition between the baryonic gas and the magnetic field, starting at z = 8, to track the evolution of magnetic fields, and compare with results of MHD simulations. We have found that for halos and cores, our results are comparable to the MHD description. For the less dense regions, the equipartition condition clearly overestimates the observed limits. In forthcoming work, we will investigate MHD simulations of cosmological evolution and amplification of seed magnetic fields, considering all relevant feedback processes and exploring turbulent dynamo amplification versus primordial mechanisms across cosmological timescales.