A Molecular Line Scan in the Hubble Deep Field North: Constraints on the
  CO Luminosity Function and the Cosmic H2 Density
  We present direct constraints on the CO luminosity function at high redshift
and the resulting cosmic evolution of the molecular gas density, $\rho_{\rm
H2}$(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 the
entire 3mm window (79-115 GHz) covers a cosmic volume of ~7000 Mpc$^3$, and
redshift ranges z<0.45, 1.01<z<1.89 and z>2. We use the rich multiwavelength
and spectroscopic database of the HDF-N to derive some of the best constraints
on CO luminosities in high redshift galaxies to date. We combine the blind CO
detections in our molecular line scan (presented in a companion paper) with
stacked CO limits from galaxies with available spectroscopic redshifts (slit or
mask spectroscopy from Keck and grism spectroscopy from HST) to give first
blind constraints on high-z CO luminosity functions and the cosmic evolution of
the H2 mass density $\rho_{\rm H2}$(z) out to redshifts z~3. A comparison to
empirical predictions of $\rho_{\rm H2}$(z) shows that the securely detected
sources in our molecular line scan already provide significant contributions to
the 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 our
observations results in cosmic molecular gas densities $\rho_{\rm H2}$(z) that
are higher than current predictions. We note however that the current
uncertainties (in particular the luminosity limits, number of detections, as
well as cosmic volume probed) are significant, a situation that is about to
change with the emerging ALMA observatory.
