We calculate the mass distribution of Primordial Black Holes (PBHs) produced during metric preheating. After inflation, the oscillations of the inflaton at the bottom of its potential source a parametric resonant instability for small-scale scalar perturbations, that may collapse into black holes. After reviewing in a pedagogical way different techniques that have been developed in the literature to compute mass distributions of PBHs, we focus on the excursion-set approach.

Cosmological and astronomical observations indicate that the majority of mass and energy density of fields in the universe are in a form which interacts extremely weakly, if at all, with light. The standard interpretation is the existence of dark matter, commonly thought to be in the form of particles not part of the standard model of particle physics. At present a firm detection of such a particle is lacking, and moreover, all these observations concern a mismatch between the observed dynamics of visible matter with its gravitational influence.

In the primordial Universe, neutrino decoupling occurs only slightly before electron-positron annihilations. This leads to an increased neutrino energy density with order 1% spectral distortions compared to the standard instantaneous decoupling approximation. A precise calculation of neutrino evolution is needed to assess its consequences on BBN, structure formation or on the CMB, and requires to take into account multiple effects such as neutrino oscillations, which represents a genuine numerical challenge. 

In this talk I will discuss cosmological first-order phase transitions. These phase transitions which proceed through the nucleation and merger of bubbles on the new phase are known to source gravitational waves. If one of these events occurred in the early universe then upcoming space based gravitational wave detectors like LISA may be able to detect the resulting gravitational wave background that remains today. In this talk I will focus on transitions in which the bubble wall accelerates until collision.

Magnetic fields are observed on virtually all astrophysical scales of the modern Universe, from planets and stars to galaxies and galaxy clusters. Observations of blazars suggest that even the intergalactic medium is permeated by magnetic fields. Such large-scale fields were most likely generated very shortly after the Big Bang and therefore are a unique window into the physics of the very early Universe.