Gravitational Dark Matter and Primordial Black Holes

Let's be frank: we all love WIMP dark matter (DM). However, thermal equilibrium may not be reached between the visible and dark sectors. The only interaction guaranteed between them is gravity. Gravitational DM could be generated by the Hawking evaporation of primordial black holes. It is typically assumed that after production, DM abundance freezes and remains constant. However, thermalization and number-changing processes in the dark sector can have a strong impact, in particular enhancing the DM population by several orders of magnitude. Here we review the impact of self-interactions from general arguments such as the conservation of energy and entropy, independently from the underlying particle physics details of the dark sector. Additionally, we study the interplay with other purely gravitational DM production mechanisms, such as the scattering of standard model states or inflatons, mediated by the $s$-channel exchange of gravitons. We show that the latter mechanism sets strong bounds, excluding large regions of the parameter space favored by primordial black hole production.