There was a time when primordial magnetic fields posed a serious
contender to explaining the origin of magnetic fields in galaxies
and on larger scales. This has changed drastically during the past
three decades, and now the dynamo origin of galactic magnetic fields is
unchallenged. Nevertheless, primordial magnetic fields might still be an
attractive possibility to understanding magnetic fields between clusters
of galaxies, which are difficult to explain by astrophysical
mechanisms such as outflows from active galactic nuclei. Primordial
magnetic fields generated during the electroweak phase transition,
for example would decay during much of their subsequent evolution,
but helicity slows down the decay by inverse cascading the field to
larger scales. Dynamo-generated magnetic fields, on the other hand,
also tend to be helical, if the dynamo operates in the presence of
rotation and stratification. In my talk, I will discuss the evolution
of magnetic fields in both cases using numerical simulations.
I will then turn to the observational signatures of helical magnetic
fields. Galactic magnetic fields can be inferred through synchrotron
radiation. To avoid distortion from Faraday rotation, shorter wavelengths
used to be of interest, but nowadays the detailed wavelength dependence
of polarized emission can be used to learn about the detailed field
structure. I will show how Faraday rotation can be used to measure
the helicity of the field with future facilities such as the square
kilometer array.
On scales of the solar system, on the other hand, in situ measurement
of magnetic fields have been carried out since the Voyager missions.
However, measuring magnetic helicity is not straightforward and requires
extra assumptions such as isotropy. I will compare these results with
solar surface measurements and discuss them in the framework of dynamo
theory.