Probing multiple populations of compact binaries with third-generation
  gravitational-wave detectors
  Third-generation (3G) gravitational-wave (GW) detectors will be able to
observe binary-black-hole mergers (BBHs) up to redshift of $\sim 30$. This
gives unprecedented access to the formation and evolution of BBHs throughout
cosmic history. In this paper we consider three sub-populations of BBHs
originating from the different evolutionary channels: isolated formation in
galactic fields, dynamical formation in globular clusters and mergers of black
holes formed from Population III (Pop III) stars at very high redshift. Using
input from populations synthesis analyses, we created two months of simulated
data of a network of 3G detectors made of two Cosmic Explorers and an Einstein
Telescope, consisting of $\sim16000$ field and cluster BBHs as well as
$\sim400$ Pop III BBHs. First, we show how one can use non-parametric models to
infer the existence and characteristic of a primary and secondary peak in the
merger rate distribution. In particular, the location and the height of the
secondary peak around $z\approx 12$, arising from the merger of Pop III
remnants, can be constrained at $\mathcal{O}(10\%)$ level. Then we perform a
modeled analysis, using phenomenological templates for the merger rates of the
three sub-population, and extract the branching ratios and the characteristic
parameters of the merger rate densities of the individual formation channels.
With this modeled method, the uncertainty on the measurement of the fraction of
Pop III BBHs can be improved to $\lesssim 10\%$, while the ratio between field
and cluster BBHs can be measured with an uncertainty of $\sim 50\%$.
