The ALMA Spectroscopic Survey in the HUDF: The Cosmic Dust and Gas Mass
  Densities in Galaxies up to $z\sim3$
  Using the deepest 1.2 mm continuum map to date in the Hubble Ultra Deep Field
obtained as part of the ALMA Spectroscopic Survey (ASPECS) large program, we
measure the cosmic density of dust and implied gas (H$_{2}+$H I) mass in
galaxies as a function of look-back time. We do so by stacking the contribution
from all $H$-band selected galaxies above a given stellar mass in distinct
redshift bins, $\rho_{\rm dust}(M_\ast>M,z)$ and $\rho_{\rm gas}(M_\ast>M,z)$.
At all redshifts, $\rho_{\rm dust}(M_\ast>M,z)$ and $\rho_{\rm
gas}(M_\ast>M,z)$ grow rapidly as $M$ decreases down to $10^{10}\,M_\odot$, but
this growth slows down towards lower stellar masses. This flattening implies
that at our stellar mass-completeness limits ($10^8\,M_\odot$ and
$10^{8.9}\,M_\odot$ at $z\sim0.4$ and $z\sim3$), both quantities converge
towards the total cosmic dust and gas mass densities in galaxies. The cosmic
dust and gas mass densities increase at early cosmic time, peak around
$z\sim2$, and decrease by a factor $\sim4$ and 7, compared to the density of
dust and molecular gas in the local universe, respectively. The contribution of
quiescent galaxies -- i.e., with little on-going star-formation -- to the
cosmic dust and gas mass densities is minor ($\lesssim10\%$). The redshift
evolution of the cosmic gas mass density resembles that of the star-formation
rate density, as previously found by CO-based measurements. This confirms that
galaxies have relatively constant star-formation efficiencies (within a factor
$\sim2$) across cosmic time. Our results also imply that by $z\sim0$, a large
fraction ($\sim90\%$) of dust formed in galaxies across cosmic time has been
destroyed or ejected to the intergalactic medium.
