Primordial Magnetic Field Effects on the CMB and Large Scale Structure
  Magnetic fields are everywhere in nature and they play an important role in
every astronomical environment which involves the formation of plasma and
currents. It is natural therefore to suppose that magnetic fields could be
present in the turbulent high temperature environment of the big bang. Such a
primordial magnetic field (PMF) would be expected to manifest itself in the
cosmic microwave background (CMB) temperature and polarization anisotropies,
and also in the formation of large- scale structure. In this review we
summarize the theoretical framework which we have developed to calculate the
PMF power spectrum to high precision. Using this formulation, we summarize
calculations of the effects of a PMF which take accurate quantitative account
of the time evolution of the cut off scale. We review the constructed numerical
program, which is without approximation, and an improvement over the approach
used in a number of previous works for studying the effect of the PMF on the
cosmological perturbations. We demonstrate how the PMF is an important
cosmological physical process on small scales. We also summarize the current
constraints on the PMF amplitude $B_\lambda$ and the power spectral index $n_B$
which have been deduced from the available CMB observational data by using our
computational framework.
