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Next generation ground-based gravitational-wave detectors will observe binaryblack hole (BBH) mergers up to redshift $z\gtrsim{}10$, probing the evolutionof compact binary (CB) mergers across cosmic time. Here, we present a newdata-driven model to estimate the cosmic merger rate density (MRD) evolution ofCBs, by coupling catalogs of CB mergers with observational constraints on thecosmic star formation rate density and on the metallicity evolution of theUniverse. We adopt catalogs of CB mergers derived from recent $N-$body andpopulation-synthesis simulations, to describe the MRD of CBs formed in youngstar clusters (hereafter, dynamical CBs) and in the field (hereafter, isolatedCBs). 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 firstand second observing run (O1 and O2) of the LIGO-Virgo collaboration, and withthe 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 consistentwith the upper limit inferred from O1 and O2. Finally, the local MRD ofdynamical 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 isolatedBNSs ($\mathcal{R}_{\rm BNS}=283^{+97}_{-75}$ Gpc$^{-3}$ yr$^{-1}$). The MRDfor 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 betweencosmic star formation rate, metallicity evolution and delay time of binarycompact objects.

The cosmic merger rate density evolution of compact binaries formed in young star clusters and in isolated binaries