A 3+1 Perturbative Approach to the Cosmic Dynamo Equation

TL;DR

This paper develops a numerical relativity-based perturbative framework to study the evolution and amplification of primordial magnetic fields in the early universe, linking seed magnetogenesis to observed cosmic magnetic fields.

Contribution

It introduces a 3+1 perturbative approach to the cosmic dynamo equation and demonstrates how velocity fields driven by scalar perturbations amplify primordial magnetic fields.

Findings

Velocity fields drive magnetic field amplification

Growth depends on cosmic medium's conductivity

Provides a computational link to primordial magnetogenesis

Abstract

In this work, we analyze the evolution of PMFs within a perturbed Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) spacetime using the formalisms of Numerical Relativity (NR). We apply the 3+1 decomposition to first-order cosmological perturbations to derive the cosmological dynamo equation under the kinematic-dynamo approximation. Our objective is to study the interaction between the seed magnetic field and the growing modes of scalar perturbations, whose associated velocity fields are evolved numerically using the software \texttt{Einstein Toolkit} and \texttt{FLRWSolver}. We find that these velocity fields effectively drive the amplification of the PMF, demonstrating that the extent of this growth is dependent on the electrical conductivity of the cosmic medium. Our findings provide a computational description linking primordial magnetogenesis to the evolution of magnetic seeds, ultimately explaining the ubiquity of large-scale magnetic fields in the universe