Primordial black holes from multi-field inflation

In this master's thesis, the formation of Primordial Black Holes (PBHs) in the context of multi-field inflation is studied. In these models, the interaction of isocurvature and curvature perturbations can lead to a significant enhancement of the latter, and to the subsequent production of PBHs. Depending on their mass, these can account for a significant fraction (or, in some cases, the entirety) of the universe's Dark Matter content. After studying the theoretical framework of generic N-field inflationary models, the focus is restricted to the two-field case, for which a few concrete realisations are analysed. A numerical code (written in Wolfram Mathematica) is developed to make quantitative predictions for the main inflationary observables, notably the scalar power spectra. Parallelly, the production of PBHs due to the dynamics of 2-field inflation is examined: their mass, as well as the fraction of Dark Matter they represent, is calculated for the models considered previously.

A next-to-leading order calculation of the impact of primordial magnetic fields into cosmological observables

In this thesis, we perform a next-to-leading order calculation of the impact of primordial magnetic fields (PMF) into the evolution of scalar cosmological perturbations and the cosmic microwave background (CMB) anisotropy. Magnetic fields are everywhere in the Universe at all scales probed so far, but their origin is still under debate. The current standard picture is that they originate from the amplification of initial seed fields, which could have been generated as PMFs in the early Universe. The most robust way to test their presence and constrain their features is to study how they impact on key cosmological observables, in particular the CMB anisotropies. The standard way to model a PMF is to consider its contribution (quadratic in the magnetic field) at the same footing of first order perturbations, under the assumptions of ideal magneto-hydrodynamics and compensated initial conditions. In the perspectives of ever increasing precision of CMB anisotropies measurements and of possible uncounted non-linear effects, in this thesis we study effects which go beyond the standard assumptions. We study the impact of PMFs on cosmological perturbations and CMB anisotropies with adiabatic initial conditions, the effect of Alfvén waves on the speed of sound of perturbations and possible non-linear behavior of baryon overdensity for PMFs with a blue spectral index, by modifying and improving the publicly available Einstein-Boltzmann code SONG, which has been written in order to take into account all second-order contributions in cosmological perturbation theory. One of the objectives of this thesis is to set the basis to verify by an independent fully numerical analysis the possibility to affect recombination and the Hubble constant.