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Black hole binaries formed dynamically in globular clusters are believed tobe one of the main sources of gravitational waves in the Universe. Here, we useour new population synthesis code, cBHBd, to determine the redshift evolutionof the merger rate density and masses of black hole binaries formed in globularclusters. We simulate $\sim 2$ million models to explore the parameter spacethat is relevant to real clusters and over all mass scales. We show that whenuncertainties on the initial cluster mass function and density are properlytaken into account, they become the two dominant factors in setting thetheoretical error bars on merger rates. Other model parameters (e.g., natalkicks, black hole masses, metallicity) have virtually no effect on the localmerger rate density, although they affect the masses of the merging blackholes. Modelling the merger rate density as a function of redshift as$R(z)=R_0(1+z)^\kappa$ at $z<2$, and marginalizing over uncertainties, we find:$R_0=7.2^{+21.5}_{-5.5}{\rm Gpc^{-3}yr^{-1}}$ and $\kappa=1.6^{+0.4}_{-0.6}$($90\%$ credibility). The rate parameters for binaries that merge inside theclusters are ${R}_{\rm 0,in}=1.6^{+1.9}_{-1.0}{\rm Gpc^{-3}yr^{-1}}$ and$\kappa_{\rm in}=2.3^{+1.3}_{-1.0}$; $\sim 20\%$ of these form as the result ofa gravitational-wave capture, implying that eccentric mergers from globularclusters contribute $\lesssim 0.4 \rm Gpc^{-3}yr^{-1}$ to the local rate. Acomparison to the merger rate reported by LIGO-Virgo shows that a scenario inwhich most of the detected black hole mergers are formed in globular clustersis consistent with current constraints, and requires initial cluster half-massdensities $\gtrsim 10^4 M_\odot \rm pc^{-3}$. Such models also reproduce theinferred primary black hole mass distribution for masses $13-30 M_\odot$, butunder-predict the data outside this range.

Merger rate of black hole binaries from globular clusters: theoretical error bars and comparison to gravitational wave data from GWTC-2