Contrasting formulations of cosmological perturbations in a magnetic
  FLRW cosmology
  In this paper we contrasted two cosmological perturbation theory formalisms,
the 1+3 covariant gauge invariant and the gauge invariant by comparing their
gauge invariant variables associated with magnetic field defined in each
approach. In the first part we give an introduction to each formalism assuming
the presence of a magnetic field. We found that gauge invariant quantities
defined by 1+3 covariant approach are related with spatial variations of the
magnetic field (defined in the gauge invariant formalism) between two closed
fundamental observers. This relation was computed by choosing the comoving
gauge in the gauge invariant approach in a magnetized universe. Furthermore, we
have derived the gauge transformations for electromagnetic potentials in the
gauge invariant approach and the Maxwell's equations have been written in terms
of these potentials.
