Limits for primordial magnetic fields
  A possible explanation for the origin of the magnetic fields observed today
in matter structures is that they were generated in the primordial universe.
After briefly revising the model of a primordial stochastic magnetic field and
sketching the main features of its time evolution in the primordial plasma, we
illustrate the current upper bounds on the magnetic field amplitude and
spectral index from Cosmic Microwave Background observations and gravitational
wave production. We conclude that a primordial magnetic field generated by a
non-causal process such as inflation with a red spectrum seems to be favoured
as a seed for the magnetic fields observed today in structures.
