Mean cosmic evolution of the molecular hydrogen density considering the five simulated boxes. The shaded region encloses the full dispersion of the five curves. The right-hand axis shows Ω_H2, the H₂ mass density normalised to the present-day critical density. Observational constraints are ASPECS (ALMA Spectroscopic Survey in the Hubble Ultra Deep Field, Decarli et al. 2020); VLASPECS (which uses the NSF’s Karl G. Jansky Very Large Array, VLA, covering part of the ASPECS footprint, Riechers et al. 2020); COLDz (VLA CO Luminosity Density at High Redshift in the COSMOS and GOODS-North fields combined; Riechers et al. 2019); PHIBBS2 (Plateau de Bure High-z Blue Sequence Survey 2, which uses the NOrthern Extended Millimeter Array – NOEMA – to observe field sources, Lenkić et al. 2020); xCOLD GASS (eXtended CO Legacy Database for the Galaxy All Sky Survey, Fletcher et al. 2021); ALMACAL-abs (blind search of CO absorbers against the ALMA Calibrator archive sources, Klitsch et al. 2019); ALMACAL-CO (CO emission-line survey Hamanowicz et al. 2023); Herschel PEP (PACS Evolutionary Probes Herschel survey in the GOODS-N -S fields, Berta et al. 2013); and UKIDS-UDS (UK InfraRed Telescope – UKIRT – Infrared Deep Sky Survey in the Ultra-Deep Survey, Garratt et al. 2021). Data listed in the top right legend do not use direct measurement of CO emission to estimate molecular masses.