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We evaluate the redshift distribution of binary black hole (BBH), black hole- neutron star binary (BHNS) and binary neutron star (BNS) mergers, exploringthe main sources of uncertainty: star formation rate (SFR) density, metallicityevolution, common envelope, mass transfer via Roche lobe overflow, natal kicks,core-collapse supernova model and initial mass function. Among binary evolutionprocesses, uncertainties on common envelope ejection have a major impact: thelocal merger rate density of BNSs varies from $\sim{}10^3$ to $\sim{}20$Gpc$^{-3}$ yr$^{-1}$ if we change the common envelope efficiency parameter from$\alpha_{\rm CE}=7$ to 0.5, while the local merger rates of BBHs and BHNSs varyby a factor of $\sim{}2-3$. The BBH merger rate changes by one order ofmagnitude, when $1 \sigma$ uncertainties on metallicity evolution are takeninto account. In contrast, the BNS merger rate is almost insensitive tometallicity. Hence, BNSs are the ideal test bed to put constraints on uncertainbinary evolution processes, such as common envelope and natal kicks. Onlymodels assuming values of $\alpha_{\rm CE}\gtrsim{}2$ and moderately low natalkicks (depending on the ejected mass and the SN mechanism), result in a localBNS merger rate density within the 90% credible interval inferred from thesecond gravitational-wave transient catalogue.

The cosmic merger rate density of compact objects: impact of star formation, metallicity, initial mass function and binary evolution