Constraining the magnetic evolutionary track of the Universe

Current gamma-ray and radio observations constrain the present-day
intergalactic magnetic field to be between 10^{-16} and 10^{-9} gauss
on parsec to megaparsec scales. Their filling factors in the voids
between galaxy clusters must have exceeded 10 to 30 percent, making it
unlikely to be produced by astrophysical mechanisms. A magnetic field
of primordial origin could have been generated in the first microseconds
of the Universe during inflation or the subsequent electroweak or quark
confinement epochs. Its comoving strength and typical scale are or will
be reflected in the spectrum of relic gravitational waves on millihertz
to nanohertz frequencies. Between generation and present-day observation,
the magnetic field must have evolved on a specific track in a diagnostic
diagram of comoving field strength versus length scale. This evolution is
described by decaying homogeneous magnetically dominated turbulence. This
is the subject of high-resolution direct numerical simulations covering
over 28 orders of magnitude in cosmic time, augmented by an improved
theoretical understanding of the turbulent decay. However, there are
still some theoretical questions such as the effects of reconnection,
and there are numerical challenges, so we need to ask when can we trust
the simulations. Also, how are the results affected by additional physics
such as the detailed generation mechanism, for example through axion-like
particles, and during the time of recombination, they must include the
interaction between photons, baryons, as well as dark matter, and of
course the changing expansion of the universe. In my talk, I will review
these recent developments and discuss ways of addressing them.