Uncovering the population of compact binary mergers and their formation pathways with gravitational waves through the Einstein Telescope

Ground-based gravitational-wave (GW) observatories have transformed our view of compact-object mergers, yet their reach still limits a comprehensive reconstruction of the processes that generate these systems. Only next-generation observatories, with order-of-magnitude improvements in sensitivity and access to lower frequencies, will be capable of radically extending this detection horizon. GW observations will make it possible to detect the complete population of binary black hole (BBH) mergers out to redshifts of $z \simeq 100$. This capability will deliver an unprecedented map of merger events across cosmic time and enable precise reconstruction of their mass and spin distributions, while for several thousand events the signal-to-noise ratio will surpass 100, enabling precision physics of BHs and neutron stars (NSs). The access to lower frequencies will also open the intermediate-mass window, detecting systems of order $\sim 10^3 M_\odot$, potentially in coordination with multi-band observations from LISA. At higher redshifts, where Population III stars have so far remained beyond reach - even for the James Webb Space Telescope - GW observations by next-generation detectors will routinely provide observations of BH mergers thought to originate from these primordial stellar populations. Such measurements are expected to play a central role in clarifying the early assembly of supermassive black holes. A single detection of a binary BH system at $z \gtrsim 30$, or of a compact object with sub-solar mass and no tidal deformability, would constitute strong evidence for the existence of primordial black holes. Such a discovery would have profound consequences for our understanding of dark matter and the early Universe. Ultimately, the GW observations will become revolutionary for identifying the physical channels responsible for compact binary formation.