Primordial black holes (PBHs) are believed to form through the gravitational collapse of overdense regions in the early Universe. They may serve as seeds for galaxy formation and are also considered one of the important candidates for cold dark matter (DM).
In particular, I will focus on several representative toy models of single-field inflation. The enhanced primordial perturbations in these models can not only produce PBHs, but also generate gravitational waves through higher-order effects. I will further extend the discussion to the possibility of a PBH-dominated era, which could leave observable signatures if PBH evaporation produces stable relics.
These studies demonstrate the significant potential of PBHs as probes of the early Universe, naturally leading to the important question of how to accurately estimate the PBH abundance. In the latter part of the talk, I will introduce a method based on peaks theory for estimating the abundance of primordial black holes. Our approach works well for arbitrary forms of the power spectrum, and by incorporating more systematic statistical methods, we expect it to provide useful cross-checks in combination with future gravitational-wave observations and related cosmological probes.