Cosmological Perturbations: Vorticity, Isocurvature and Magnetic Fields
  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.
