The cosmic star formation history (CSFH) increased from early epochs (z~6), 
peaked around z=1-3 (the `epoch of galaxy assembly'), then decreased by an 
order of magnitude until present age. What drives this evolution? 
We investigate whether the trend in CSFH is driven by the evolution of the 
molecular gas content in galaxies. We performed the first molecular scan in 
a region of the Hubble Deep Field North (HDF-N), by scanning the 3mm window 
(79-115 GHz) using the IRAM Plateu de Bure Interferometer. Our goal was to 
put first direct constraints on the molecular gas functions, as traced by 
carbon monoxide (CO), at high redshift. We found 17 line candidates, and 
estimated that only up to 4 of them are spurious. By cross-matching with 
available multi-wavelength photometric and spectroscopic information in the 
HDF-N, and with dedicated follow-up observations at 2mm, we could pin down 
the line identification (thus, the redshift of the associated galaxies), 
and estimate physical quantities (e.g., location in the global star-formation 
law; molecular gas fraction; depletion time). More importantly, we could set 
first observational constraints on the CO luminosity functions up to z~3. 
Our results are in broad agreement with available models showing an enhanced 
cosmic abundance of molecular gas at high z. Such evolution could be even 
steeper than what predicted by current models, if all the line candidates 
discovered in our study were to be confirmed. More constraints will come 
from our follow-up observations (including a parallel 30-38 GHz scan of the 
GOODS-North area using the Jansky Very Large Array) and from a recently 
approved ALMA cycle 2 3mm project aim at repeating our 3mm scan experiment 
in a region of the Hubble Ultra Deep Field.