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tokens: review by Somerville Davé 2015 ). At z ∼ 5–7, the excess of bright sources compared to the semi-analytical predictions appears to be even more pronounced than at lower redshifts but we caution that the most constraining measurement is based on a small number of sources only, and thus needs to be put on a firmer statistical footing. Meanwhile, the observations at z ∼ 2–3 appear to be consistent with Vallini et al.’s ( 2016 ) empirical predictions, and thus with what is expected from estimates of dust-obscured star formation activity at high redshift based on infrared luminosity functions. 4.2.2. Cold Gas Density of the Universe The observational constraints on the evolution of the cold gas density with redshift remain in agreement with both semi-analytical (Obreschkow et al. 2009 ; Lagos et al. 2011 , 2012 ; Popping et al. 2014a , 2014b ) and empirical (Sargent et al. 2012 , 2014 ) model predictions at z ∼ 2–3. Since most of the semi-analytical models include a varying α CO between individual galaxies, a simple interpretation of the consistency—despite the disagreement in the luminosity function estimates—remains challenging. In addition, the predictions do not account for the sensitivity limits of the CO surveys, or uncertainties due to cosmic variance. Given the differences in the CO luminosity functions between models and observations at high z , this effect could in principle lead to up to a factor of a few difference in the corresponding gas densities at high redshift. However, as discussed in Section 3.4 , the impact of the sensitivity limits, which would bias the measurements toward lower values, appears to be relatively minor based on the preferred model Schechter function fits to the COLDz data. Meanwhile, cosmic variance due to large-scale structure in the distribution of gas-rich galaxies (which is assumed to be uniform in our analysis) could bias the measurements either low or high. To obtain an approximate estimate of systematic uncertainties introduced by cosmic variance, we follow the prescription by Driver Robotham ( 2010 ), based on the distribution of galaxies near the characteristic stellar mass at a given redshift. 40 40 This method is based on a generalized expression (their Equation (4)) calibrated through an examination of galaxies within ±1 mag of the characteristic optical magnitude out to z ∼ 0.1 in the Sloan Digital Sky Survey (SDSS), which represent the most common galaxies at a given redshift. See cosmocalc.icrar.org for additional details. The field sizes and CO( J = 1 → 0) redshift ranges in Table 1 are used for all calculations. Including both Poisson uncertainty and cosmic variance scaled to the volume of the COLDz survey, we find a sample variance uncertainty of ∼30%–40% and ∼25% for the COSMOS and GOODS-North fields, respectively. Alternatively, adapting results based on models of the evolution of the most massive galaxies (i.e., M ⋆ > 10 11 M ⊙ ) by Moster et al. ( 2011 ) 41 41 For our estimate, we have made