A non-perturbative study of the evolution of cosmic magnetised sources
  We undertake a hydrodynamical study of a mixture of tightly coupled
primordial radiation, neutrinos, baryons, electrons and positrons, together
with a gas of already decoupled dark matter WIMPS and an already existing
"frozen" magnetic field in the infinite conductivity regime. Considering this
cosmic fluid as the source of a homogeneous but anisotropic Bianchi I model, we
describe its interaction with the magnetic field by means of suitable equations
of state that are appropriate for the particle species of the mixture between
the end of the leptonic era and the beginning of the radiation-dominated epoch.
Fulfilment of observational bounds on the magnetic field intensity yields a
"near FLRW" (but strictly non-perturbative) evolution of the geometric,
kinematic and thermodynamical variables. This evolution is roughly comparable
to the weak field approximation in linear perturbations on a spatially flat
FLRW background of sources in which the frozen magnetic fields are coherent
over very large supra-horizon scales. Our approach and results may provide
interesting guidelines in potential situations in which non-perturbative
methods are required to study the interaction between magnetic fields and the
cosmic fluid.
