Equivalence between formulations in Cosmological Perturbation Theory: The primordial magnetic fields as an example

TL;DR

This paper compares two formalisms in cosmological perturbation theory, demonstrating their equivalence and applying them to analyze the evolution of primordial magnetic fields, with implications for understanding magnetogenesis.

Contribution

It establishes the equivalence between the 1+3 covariant and gauge invariant formalisms in cosmological perturbation theory, specifically applied to primordial magnetic fields.

Findings

Demonstrated the equivalence of the two formalisms

Derived Maxwell's equations in the context of cosmological perturbations

Analyzed the evolution of primordial magnetic fields in Poisson gauge

Abstract

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.