  Arguably the main challenge of galactic magnetism studies is to explain how
the interstellar medium of galaxies reaches energetic equipartition despite the
extremely weak cosmic primordial magnetic fields that are originally predicted
to thread the inter-galactic medium. Previous numerical studies of isolated
galaxies suggest that a fast dynamo amplification might suffice to bridge the
gap spanning many orders of magnitude in strength between the weak early
Universe magnetic fields and the ones observed in high redshift galaxies. To
better understand their evolution in the cosmological context of hierarchical
galaxy growth, we probe the amplification process undergone by the cosmic
magnetic field within a spiral galaxy to unprecedented accuracy by means of a
suite of constrained transport magnetohydrodynamical adaptive mesh refinement
cosmological zoom simulations with different stellar feedback prescriptions. A
galactic turbulent dynamo is found to be naturally excited in this cosmological
environment, being responsible for most of the amplification of the magnetic
energy. Indeed, we find that the magnetic energy spectra of simulated galaxies
display telltale inverse cascades. Overall, the amplification process can be
divided in three main phases, which are related to different physical
mechanisms driving galaxy evolution: an initial collapse phase, an
accretion-driven phase, and a feedback-driven phase. While different feedback
models affect the magnetic field amplification differently, all tested models
prove to be subdominant at early epochs, before the feedback-driven phase is
reached. Thus the three-phase evolution paradigm is found to be quite robust
vis-a-vis feedback prescriptions.
