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We present direct constraints on the CO luminosity function at high redshiftand the resulting cosmic evolution of the molecular gas density, $\rho_{\rmH2}$(z), based on a blind molecular line scan in the Hubble Deep Field North(HDF-N) using the IRAM Plateau de Bure Interferometer. Our line scan of theentire 3mm window (79-115 GHz) covers a cosmic volume of ~7000 Mpc$^3$, andredshift ranges z<0.45, 1.01<z<1.89 and z>2. We use the rich multiwavelengthand spectroscopic database of the HDF-N to derive some of the best constraintson CO luminosities in high redshift galaxies to date. We combine the blind COdetections in our molecular line scan (presented in a companion paper) withstacked CO limits from galaxies with available spectroscopic redshifts (slit ormask spectroscopy from Keck and grism spectroscopy from HST) to give firstblind constraints on high-z CO luminosity functions and the cosmic evolution ofthe H2 mass density $\rho_{\rm H2}$(z) out to redshifts z~3. A comparison toempirical predictions of $\rho_{\rm H2}$(z) shows that the securely detectedsources in our molecular line scan already provide significant contributions tothe predicted $\rho_{\rm H2}$(z) in the redshift bins <z>~1.5 and <z>~2.7.Accounting for galaxies with CO luminosities that are not probed by ourobservations results in cosmic molecular gas densities $\rho_{\rm H2}$(z) thatare higher than current predictions. We note however that the currentuncertainties (in particular the luminosity limits, number of detections, aswell as cosmic volume probed) are significant, a situation that is about tochange with the emerging ALMA observatory.

A Molecular Line Scan in the Hubble Deep Field North: Constraints on the CO Luminosity Function and the Cosmic H2 Density