  Nowdays, Cosmological Perturbation Theory is a standard and useful tool in
theoretical cosmology. In this work, we compare the 1+3 covariant formalism in
perturbation theory (Ellis et al.) to the gauge invariant approach (Bruni et
al.), and we show the equivalence of these formalisms to fix the choice of the
perturbed variables (gauge choice) in magnetogenesis. We analyze the evolution
of primordial magnetic fields through perturbation theory and we discuss the
similarities and differences between these two approaches. We get the Maxwell's
equations and show a cosmic dynamo like equation written in Poisson gauge,
computing the evolution of primordial magnetic fields. Finally, prospects
around these formalisms in the study of magnetogenesis are discussed.
