Cosmic magnetic fields from density perturbations

Magnetic fields are observed on nearly all scales in the Universe, from stars and galaxies up to galaxy clusters and even beyond. The origin of cosmic magnetic fields remains an open question; however, a large class of models puts its origin in the very early Universe. The most conservative physical mechanism for such primordial seed-field generation was proposed by Harrison; his mechanism relies on the fact that weak magnetic fields are generated during the radiation era in regions that are characterized by nonvanishing vorticity. A magnetic dynamo amplifying this initial seed magnetic field could explain the present-day strength of the galactic magnetic field. Nevertheless, it is still an unresolved query the how and when this seed magnetic field was created. Observations of the cosmic microwave background (CMB) provide a window to the early Universe and might therefore be able to tell us whether cosmic magnetic fields are of a primordial cosmological origin and, at the same time, constrain its parameters. In Chapter 1, we recall some notions about neutral fluids governed by hydrodynamic equations and about charged fluids governed by magnetohydrodynamic equations. In Chapter 2, we look at observations of magnetic fields at different scales, at the different seed field hypothesis and at some astrophysical method, like mean field dynamo theory, in order to explain the amplification of the initial seed magnetic field. In Chapter 3, we focus on standard cosmology (FLRW), inflation dynamics and density perturbations produced by quantum fluctuations, perturbation theory and some typical gauges used in cosmology. In Chapter 4, we obtain the energy-momentum equation up to second order in perturbation theory in the Poisson gauge, we briefly recall the Harrison’s mechanism and derive the seed magnetic field and its spectrum as a function of the primordial density perturbations produced during inflation.