Constraints on the cosmic molecular gas mass density ρ_H2 based on CO abundance measurements across redshifts 0–4. We show COMAP Season 1 and Season 2 constraints on ⟨T⟩ converted based on Eq. (13), including both the two-parameter analysis upper limit and the five-parameter UM+COLDz+COPSS+COMAP S2 result. For comparison, we also show past results from untargeted interferometric CO line searches (boxes) – ASPECS (Decarli et al. 2020), PHIBBS2 (Lenkić et al. 2020), and COLDz (Riechers et al. 2019) – as well as interferometric CO LIM surveys (uncapped error bars) – COPSS (Keating et al. 2016) and mmIME (Keating et al. 2020). In addition, we show a best-fit model describing results from stacked 850 μm luminosities of galaxies at redshifts 0–2.5 (Garratt et al. 2021). All results use α_CO = 3.6 M_⊙ (K km s⁻¹ pc⁻²)⁻¹ (cf. Daddi et al. 2010) except COPSS, which uses a conversion of α_CO = 4.3 M_⊙ (K km s⁻¹ pc⁻²)⁻¹ (cf. Bolatto et al. 2013), and Garratt et al. (2021), who use α_CO = 6.5 M_⊙ (K km s⁻¹ pc⁻²)⁻¹ as promoted by Scoville et al. (2016).