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We are just starting to understand the physical processes driving thedramatic change in cosmic star-formation rate between $z\sim 2$ and the presentday. A quantity directly linked to star formation is the molecular gas density,which should be measured through independent methods to explore variations dueto cosmic variance and systematic uncertainties. We use intervening COabsorption lines in the spectra of mm-bright background sources to provide acensus of the molecular gas mass density of the Universe. The data used in thiswork are taken from ALMACAL, a wide and deep survey utilizing the ALMAcalibrator archive. While we report multiple Galactic absorption lines and oneintrinsic absorber, no extragalactic intervening molecular absorbers aredetected. However, thanks to the large redshift path surveyed ($\Delta z=182$),we provide constraints on the molecular column density distribution functionbeyond $z\sim 0$. In addition, we probe column densities of N(H$_2$) >10$^{16}$ atoms~cm$^{-2}$, five orders of magnitude lower than in previousstudies. We use the cosmological hydrodynamical simulation IllustrisTNG to showthat our upper limits of $\rho ({\rm H}_2)\lesssim 10^{8.3} \text{M}_{\odot}\text{Mpc}^{-3}$ at $0 < z \leq 1.7$ already provide new constraints on currenttheoretical predictions of the cold molecular phase of the gas. These resultsare in agreement with recent CO emission-line surveys and are complementary tothose studies. The combined constraints indicate that the present decrease ofthe cosmic star-formation rate history is consistent with an increasingdepletion of molecular gas in galaxies compared to $z\sim 2$.

ALMACAL VI: Molecular gas mass density across cosmic time via a blind search for intervening molecular absorbers