  The metallicity distributions of globular cluster (GC) systems in galaxies
are a critical test of any GC formation scenario. In this work, we investigate
the predicted GC metallicity distributions of galaxies in the MOdelling Star
cluster population Assembly In Cosmological Simulations within EAGLE
(E-MOSAICS) simulation of a representative cosmological volume ($L = 34.4$
comoving Mpc). We find that the predicted GC metallicity distributions and
median metallicities from the fiducial E-MOSAICS GC formation model agree well
the observed distributions, except for galaxies with masses $M_\ast \sim 2
\times 10^{10}$ M$_\odot$, which contain an overabundance of metal-rich GCs.
The predicted fraction of galaxies with bimodal GC metallicity distributions
($37 \pm 2$ per cent in total; $45 \pm 7$ per cent for $M_\ast > 10^{10.5}$
M$_\odot$) is in good agreement with observed fractions ($44^{+10}_{-9}$ per
cent), as are the mean metallicities of the metal-poor and metal-rich peaks. We
show that, for massive galaxies ($M_\ast > 10^{10}$ M$_\odot$), bimodal GC
distributions primarily occur as a result of cluster disruption from
initially-unimodal distributions, rather than as a result of cluster formation
processes. Based on the distribution of field stars with GC-like abundances in
the Milky Way, we suggest that the bimodal GC metallicity distribution of Milky
Way GCs also occurred as a result of cluster disruption, rather than formation
processes. We conclude that separate formation processes are not required to
explain metal-poor and metal-rich GCs, and that GCs can be considered as the
surviving analogues of young massive star clusters that are readily observed to
form in the local Universe today.
