The primordial magnetic field in our cosmic backyard
  We reconstruct the 3D structure of magnetic fields, which were seeded by
density perturbations during the radiation dominated epoch of the Universe and
later on were evolved by structure formation. To achieve this goal, we rely on
three dimensional initial density fields inferred from the 2M++ galaxy
compilation via the Bayesian $\texttt{BORG}$ algorithm. Using those, we
estimate the magnetogenesis by the so called Harrison mechanism. This effect
produced magnetic fields exploiting the different photon drag on electrons and
ions in vortical motions, which are exited due to second order perturbation
effects in the Early Universe. Subsequently we study the evolution of these
seed fields through the non-linear cosmic structure formation by virtue of a
MHD simulation to obtain a 3D estimate for the structure of this primordial
magnetic field component today. At recombination we obtain a reliable lower
limit on the large scale magnetic field strength around $10^{-23} \mathrm{G}$,
with a power spectrum peaking at about $ 2\, \mathrm{Mpc}^{-1}h$ in comoving
scales. At present we expect this evolved primordial field to have strengthts
above $\approx 10^{-27}\, \mathrm{G}$ and $\approx 10^{-29}\, \mathrm{G}$ in
clusters of galaxies and voids, respectively. We also calculate the
corresponding Faraday rotation measure map and show the magnetic field
morphology and strength for specific objects of the Local Universe.
