Evolution of the cosmic matter density field with a primordial magnetic field

TL;DR

This paper investigates how primordial magnetic fields influence the evolution of the cosmic matter density field, the matter power spectrum, and CMB polarization, emphasizing the importance of including zero order PMF effects in linear perturbation theory.

Contribution

It introduces the first application of zero order PMF effects to theoretical matter power spectrum calculations, revising previous models for more accurate cosmological predictions.

Findings

Zero order PMF effects delay matter-radiation equality.

PMF influences the matter power spectrum via the Meszaros effect and potential decay.

Including zero order effects improves understanding of CMB polarization and weak lensing.

Abstract

A cosmological magnetic field affects the time evolution of the cosmic matter density field. The squared Alfven velocity of the cosmic fluid is proportional to an ensemble average energy density of a primordial magnetic field (PMF), and it prevents the matter density field from collapsing in the horizon scale. The matter-radiation equality time also is delayed by the presence of an ensemble average energy density of a PMF. The ensemble average energy density of the PMF also affects the matter power spectrum (MPS) through the Meszaros effect and the potential decay. Since the ensemble average energy density of the PMF is not a first order perturbation but a zero order source in the linear perturbation equations for the cosmology, to correctly understand the overall effects of the PMF on the MPS, we should significantly revise previous approaches to research for the MPS with the PMF by considering both the effects of the zero and first order sources from the PMF in the linear perturbation theory. We apply the effects of the zero order sources from the PMF to theoretical computations of the MPS for the first time. We also analyze the overall PMF effects on the MPS. The CMB polarizations are affected the weak lensing. The weak lensing is determined by the MPS. Therefore, we have to consider the zero order sources of the PMF to gain a correct understanding not only of the MPS but also the CMB polarization.