Cosmological perturbations: Vorticity, isocurvature and magnetic fields

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.

General perfect fluid perturbations of homogeneous and orthogonal locally rotationally symmetric class II cosmologies

“…For the exact equations with a general energy momentum tensor in the 1+1+2 formalism see [10], and for the theory of relativistic imperfect fluids [50][51][52]. Since a heat flow alone cannot generate vorticity to first order in perturbation theory, [36,37], it would then be of interest to consider also second order perturbations. For works on second order perturbations in covariant perturbation theory see, e.g.…”

“…For generation mechanisms due to entropy flow see e.g. [36,37] or from N-body simulations see [47]. However, as seen from section V, an already existing vorticity will act as source terms in the evolution equations for the density and electric and magnetic parts of the Weyl tensor, and may hence influence the growth of structures and give imprints on sonic and gravitational waves.…”

“…For works on vorticity perturbations on Robertson-Walker backgrounds see e.g. [21,34,[36][37][38][39].…”

Cosmic voids and BAO with relative baryon-CDM perturbations

“…★ Email:hkhorami@sissa.it Liddle & Mazumdar (2000); Langlois & Riazuelo (2000); Notari & Riotto (2002); Lyth et al (2003); Ferrer et al (2004); Li et al (2009); Grin et al (2011); Valiviita et al (2012); Huston & Christopherson (2014); Christopherson (2014); He et al (2015); Heinrich & Schmittfull (2019); Barreira et al (2020b)). However, in this work, we do not treat these CIPs, and we focus only on relative baryon-CDM perturbations induced by photon pressure prior to recombination.…”

Super-inflation and generation of first order vector perturbations in ELKO

“…Unlike the first order perturbation, it has been observed that in the case of second order perturbation theory the vector modes can be sourced and vorticity can be generated [9][10][11][12] even in the standard scalar field driven inflationary theory.…”