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The formation histories of globular clusters (GCs) are a key diagnostic forunderstanding their relation to the evolution of the Universe through cosmictime. We use the suite of 25 cosmological zoom-in simulations of present-dayMilky Way-mass galaxies from the E-MOSAICS project to study the formationhistories of stars, clusters, and GCs, and how these are affected by theenvironmental dependence of the cluster formation physics. We find that themedian lookback time of GC formation in these galaxies is ${\sim}10.73~$Gyr($z=2.1$), roughly $2.5~$Gyr earlier than that of the field stars(${\sim}8.34~$Gyr or $z=1.1$). The epoch of peak GC formation is mainlydetermined by the time evolution of the maximum cluster mass, which depends onthe galactic environment and largely increases with the gas pressure. Differentmetallicity subpopulations of stars, clusters and GCs present overlappingformation histories, implying that star and cluster formation representcontinuous processes. The metal-poor GCs ($-2.5<[\rm Fe/H]<-1.5$) of ourgalaxies are older than the metal-rich GC subpopulation ($-1.0<[\rmFe/H]<-0.5$), forming $12.13~$Gyr and $10.15~$Gyr ago ($z=3.7$ and $z=1.8$),respectively. The median ages of GCs are found to decrease gradually withincreasing metallicity, which suggests different GC metallicity subpopulationsdo not form independently and their spatial and kinematic distributions are theresult of their evolution in the context of hierarchical galaxy formation andevolution. We predict that proto-GC formation is most prevalent at $2\lesssim z\lesssim 3$, which could be tested with observations of lensed galaxies usingJWST.

Formation histories of stars, clusters and globular clusters in the E-MOSAICS simulations