We introduce a new mechanism for generating magnetic fields in the recombination era. This Harrison-like mechanism utilizes vorticity in baryons that is sourced through the Bose-Einstein condensate of axions via gravitational interactions. The magnetic fields generated are on the galactic scales $sim 10,{rm kpc}$ and have a magnitude of the order of $Bsim10^{-23},{rm G}$ today. The field has a greater magnitude than those generated from other mechanisms relying on second order perturbation theory, and is sufficient to provide a seed for battery mechanisms.
We consider a model of the early universe which consists of two scalar fields: the inflaton, and a second field which drives the stabilisation of the Planck mass (or gravitational constant). We show that the non-minimal coupling of this second field to the Ricci scalar sources a non-adiabatic pressure perturbation. By performing a fully numerical calculation we find, in turn, that this boosts the amplitude of the primordial power spectrum after inflation.
Working with perturbations about an FLRW spacetime, we compute the gauge-invariant curvature perturbation to second order solely in terms of scalar field fluctuations. Using the curvature perturbation on uniform density hypersurfaces as our starting point, we give our results in terms of field fluctuations in the flat gauge, incorporating both large and small scale behaviour. For ease of future numerical implementation we give our result in terms of the scalar field fluctuations and their time derivatives.
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 Croccos 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.
Magnetic fields are present on all scales in the Universe. While we understand the processes which amplify the fields fairly well, we do not have a natural mechanism to generate the small initial seed fields. By using fully relativistic cosmological perturbation theory and going beyond the usual confines of linear theory we show analytically how magnetic fields are generated. This is the first analytical calculation of the magnetic field at second order, using gauge-invariant cosmological perturbation theory, and including all the source terms. To this end, we have rederived the full set of governing equations independently. Our results suggest that magnetic fields of the order of $10^{-30}$ G can be generated (although this depends on the small scale cut-off of the integral), which is largely in agreement with previous results that relied upon numerical calculations. These fields are likely too small to act as the primordial seed fields for dynamo mechanisms.
Inflationary models involving more than one scalar field naturally produce isocurvature perturbations. However, while these are fairly well studied, less is known about their evolution through the reheating epoch, when the inflationary fields decay into the standard constituents of the present universe. In this paper, by modelling reheating perturbatively, we calculate the power spectrum of the non-adiabatic pressure perturbation in three different inflationary models. We show that the isocurvature can grow large initially, but decays faster than the pressure perturbations. When reheating ends, the isocurvature is negligible for the double quadratic and double quartic inflationary models. For the product exponential potential, which features large isocurvature at the end of inflation, the isocurvature decays during reheating and is around five orders of magnitudes smaller than the pressure perturbation at the end of reheating.
How much does the curvature perturbation change after it leaves the horizon, and when should one evaluate the power spectrum? To answer these questions we study single field inflation models numerically, and compare the evolution of different curvature perturbations from horizon crossing to the end of inflation. We find that e.g. in chaotic inflation, the amplitude of the comoving and the curvature perturbation on uniform density hypersurfaces differ by up to 180 % at horizon crossing assuming the same amplitude at the end of inflation, and that it takes approximately 3 efolds for the curvature perturbation to be within 1 % of its value at the end of inflation.
Non-adiabatic pressure perturbations naturally occur in models of inflation consisting of more than one scalar field. The amount of non-adiabatic pressure present at the end of inflation can have observational consequences through changes in the curvature perturbation, the generation of vorticity and subsequently the sourcing of B-mode polarisation. In this work, based on a presentation at the 13th Marcel Grossmann Meeting, we give a very brief overview of non-adiabatic pressure perturbations in multi-field inflationary models and describe our recent calculation of the spectrum of isocurvature perturbations generated at the end of inflation for different models which have two scalar fields.
Vorticity is ubiquitous in nature however, to date, studies of vorticity in cosmology and the early universe have been quite rare. In this paper, based on a talk in session CM1 of the 13th Marcel Grossmann Meeting, we consider vorticity generation from scalar cosmological perturbations of a perfect fluid system. We show that, at second order in perturbation theory, vorticity is sourced by a coupling between energy density and entropy gradients, thus extending a well-known feature of classical fluid dynamics to a relativistic cosmological framework. This induced vorticity, sourced by isocurvature perturbations, may prove useful in the future as an additional discriminator between inflationary models.
Currently, most of the numerical simulations of structure formation use Newtonian gravity. When modelling pressureless dark matter, or `dust, this approach gives the correct results for scales much smaller than the cosmological horizon, but for scenarios in which the fluid has pressure this is no longer the case. In this article, we present the correspondence of perturbations in Newtonian and cosmological perturbation theory, showing exact mathematical equivalence for pressureless matter, and giving the relativistic corrections for matter with pressure. As an example, we study the case of scalar field dark matter which features non-zero pressure perturbations. We discuss some problems which may arise when evolving the perturbations in this model with Newtonian numerical simulations and with CMB Boltzmann codes.
