Cosmological Perturbations: Vorticity, Isocurvature and Magnetic Fields

TL;DR

This paper reviews how non-adiabatic pressure perturbations in cosmological models can generate vorticity and magnetic fields, highlighting the importance of second-order perturbation theory in understanding early universe phenomena.

Contribution

It demonstrates that scalar perturbations can produce vorticity and magnetic fields through second-order effects, extending classical fluid mechanics principles to cosmology.

Findings

Vorticity is generated by scalar perturbations at second order.

Magnetic fields can arise from higher order perturbations, but are too weak to be primordial seeds.

Non-adiabatic pressure perturbations play a key role in vorticity and magnetic field generation.

Abstract

In this paper I review some recent, interlinked, work undertaken using cosmological perturbation theory -- a powerful technique for modelling inhomogeneities in the Universe. The common theme which underpins these pieces of work is the presence of non-adiabatic pressure, or entropy, perturbations. After a brief introduction covering the standard techniques of describing inhomogeneities in both Newtonian and relativistic cosmology, I discuss the generation of vorticity. As in classical fluid mechanics, vorticity is not present in linearized perturbation theory (unless included as an initial condition). Allowing for entropy perturbations, and working to second order in perturbation theory, I show that vorticity is generated, even in the absence of vector perturbations, by purely scalar perturbations, the source term being quadratic in the gradients of first order energy density and isocurvature, or non-adiabatic pressure perturbations. This generalizes Crocco's theorem to a cosmological setting. I then introduce isocurvature perturbations in different models, focusing on the entropy perturbation in standard, concordance cosmology, and in inflationary models involving two scalar fields. As the final topic, I investigate magnetic fields, which are a potential observational consequence of vorticity in the early universe. I briefly review some recent work on including magnetic fields in perturbation theory in a consistent way. I show, using solely analytical techniques, that magnetic fields can be generated by higher order perturbations, albeit too small to provide the entire primordial seed field, in agreement with some numerical studies. I close with a summary and some potential extensions of this work.