  We study the evolution of primordial magnetic fields in an expanding cosmic
plasma. For this purpose we present a comprehensive theoretical model to
consider the evolution of MHD turbulence that can be used over a wide range of
physical conditions, including cosmological and astrophysical applications. We
model different types of decaying cosmic MHD turbulence in the expanding
universe and characterize the large-scale magnetic fields in such a medium.
Direct numerical simulations of freely decaying MHD turbulence are performed
for different magnetogenesis scenarios: magnetic fields generated during cosmic
inflation as well as electroweak and QCD phase transitions in the early
universe.
  Magnetic fields and fluid motions are strongly coupled due to the high
Reynolds number in the early universe. Hence, we abandon the simple adiabatic
dilution model to estimate magnetic field amplitudes in the expanding universe
and include turbulent mixing effects on the large-scale magnetic field
evolution. Numerical simulations have been carried out for non-helical and
helical magnetic field configurations. The numerical results show the
possibility of inverse transfer of energy in magnetically dominated non-helical
MHD turbulence. On the other hand, decay properties of helical turbulence
depend on whether the turbulent magnetic field is in a weakly or a fully
helical state.
  Our results show that primordial magnetic fields can be considered as a seed
for the observed large-scale magnetic fields in galaxies and clusters. Bounds
on the magnetic field strength are obtained and are consistent with the upper
and lower limits set by observations of extragalactic magnetic fields.
