The cosmic merger rate density evolution of compact binaries formed in
  young star clusters and in isolated binaries
  Next generation ground-based gravitational-wave detectors will observe binary
black hole (BBH) mergers up to redshift $z\gtrsim{}10$, probing the evolution
of compact binary (CB) mergers across cosmic time. Here, we present a new
data-driven model to estimate the cosmic merger rate density (MRD) evolution of
CBs, by coupling catalogs of CB mergers with observational constraints on the
cosmic star formation rate density and on the metallicity evolution of the
Universe. We adopt catalogs of CB mergers derived from recent $N-$body and
population-synthesis simulations, to describe the MRD of CBs formed in young
star clusters (hereafter, dynamical CBs) and in the field (hereafter, isolated
CBs). The local MRD of dynamical BBHs is $\mathcal{R}_{\rm BBH}=64^{+34}_{-20}$
Gpc$^{-3}$ yr$^{-1}$, consistent with the 90% credible interval from the first
and second observing run (O1 and O2) of the LIGO-Virgo collaboration, and with
the local MRD of isolated BBHs ($\mathcal{R}_{\rm BBH}=50^{+71}_{-37}$
Gpc$^{-3}$ yr$^{-1}$). The local MRD of dynamical and isolated black hole -
neutron star binaries is $\mathcal{R}_{\rm BHNS}=41^{+33}_{-23}$ and
$49^{+48}_{-34}$~Gpc$^{-3}$ yr$^{-1}$, respectively. Both values are consistent
with the upper limit inferred from O1 and O2. Finally, the local MRD of
dynamical binary neutron stars (BNSs, $\mathcal{R}_{\rm BNS}=151^{+59}_{-38}$
Gpc$^{-3}$ yr$^{-1}$) is a factor of two lower than the local MRD of isolated
BNSs ($\mathcal{R}_{\rm BNS}=283^{+97}_{-75}$ Gpc$^{-3}$ yr$^{-1}$). The MRD
for all CB classes grows with redshift, reaching its maximum at $z \in
[1.5,2.5]$, and then decreases. This trend springs from the interplay between
cosmic star formation rate, metallicity evolution and delay time of binary
compact objects.
