ALMA Lensing Cluster Survey: Deep 1.2 mm Number Counts and Infrared Luminosity Functions at $z\simeq1-8$

We present a statistical study of 180 dust continuum sources identified in 33 massive cluster fields by the ALMA Lensing Cluster Survey (ALCS) over a total of 133 arcmin$^{2}$ area, homogeneously observed at 1.2 mm. ALCS enables us to detect extremely faint mm sources by lensing magnification, including near-infrared (NIR) dark objects showing no counterparts in existing {\it Hubble Space Telescope} and {\it Spitzer} images. The dust continuum sources belong to a blind sample ($N=141$) with S/N $\gtrsim$ 5.0 (a purity of $>$ 0.99) or a secondary sample ($N=39$) with S/N= $4.0-5.0$ screened by priors. With the blind sample, we securely derive 1.2-mm number counts down to $\sim7$ $\mu$Jy, and find that the total integrated 1.2mm flux is 20.7$^{+8.5}_{-6.5}$ Jy deg$^{-2}$, resolving $\simeq$ 80 % of the cosmic infrared background light. The resolved fraction varies by a factor of $0.6-1.1$ due to the completeness correction depending on the spatial size of the mm emission. We also derive infrared (IR) luminosity functions (LFs) at $z=0.6-7.5$ with the $1/V_{\rm max}$ method, finding the redshift evolution of IR LFs characterized by positive luminosity and negative density evolution. The total (=UV+IR) cosmic star-formation rate density (SFRD) at $z>4$ is estimated to be $161^{+25}_{-21}$ % of the established measurements, which were almost exclusively based on optical$-$NIR surveys. Although our general understanding of the cosmic SFRD is unlikely to change beyond a factor of 2, these results add to the weight of evidence for an additional ($\approx 60$ %) SFRD component contributed by the faint-mm population, including NIR dark objects.