Title:
Some Aspects of Cosmic Magnetic Field Evolution

Abstract:
Magnetic fields are ubiquitous in the Universe. Their origin and evolution
are still not very well understood and are subject of active research that
employs both numerical and analytical methods.
We discuss some aspects that can be relevant for cosmological and astrophysical
magnetic fields, such as magnetic helicity, inverse cascades and their
influence on magnetic field coherence length which is relevant, for example,
for the propagation of cosmic rays and electromagnetic cascades. Furthermore,
an asymmetry between left- and right-chiral lepton states can lead to the
so called chiral magnetic effect in which magnetic fields can undergo an
exponential growth phase, similar to the dynamo effect. This effect may
play a role in dense systems such as hot neutron stars and in the early Universe.
Many open questions, however, remain as will also be shown.