From primordial seed magnetic fields to the galactic dynamo
  The origin and maintenance of coherent magnetic fields in the Universe is
reviewed with an emphasis on the possible challenges that arise in their
theoretical understanding. We begin with the interesting possibility that
magnetic fields originated at some level from the early universe. This could be
during inflation, the electroweak or the quark-hadron phase transitions. These
mechanisms can give rise to fields which could be strong, but often with much
smaller coherence scales than galactic scales. Their subsequent turbulent decay
decreases their strength but increases their coherence. We then turn to
astrophysical batteries which can generate seed magnetic fields. Here the
coherence scale can be large, but the field strength is generally very small.
These seed fields need to be further amplified and maintained by a dynamo to
explain observed magnetic fields in galaxies. Basic ideas behind both small and
large-scale turbulent dynamos are outlined. The small-scale dynamo may help
understand the first magnetization of young galaxies, while the large-scale
dynamo is important for the generation of fields with scales larger than the
stirring scale, as observed in nearby disk galaxies. The current theoretical
challenges that turbulent dynamos encounter and their possible resolution are
discussed.
