COPSS II: The Molecular Gas Content of Ten Million Cubic Megaparsecs at Redshift z ~ 3

We present a measurement of the abundance of carbon monoxide in the early universe, utilizing the final results from the CO Power Spectrum Survey (COPSS). Between 2013 and 2015, we performed observations with the Sunyaev–Zel'dovich Array to measure aggregate CO emission from z ~ 3 galaxies with the intensity mapping technique. Data were collected on 19 fields, covering an area of 0.7 square degrees, over the frequency range 27-35 GHz. With these data, along with data analyzed in COPSS I, we are able to observe the CO(1–0) transition within the redshift range z = 2.3-3.3 for spatial frequencies between k=0.5-10 h Mpc}^(-1), spanning a comoving volume of 4.9 x 10^6 h^(-3) Mpc^(-3). We present estimates of contributions from continuum sources and ground illumination within our measurement. We constrain the amplitude of the CO power spectrum to P_(CO) = 3.0_(-1.3)^(+1.3) x 10^3 µK^2 (h^(-1) Mpc)^3, or Δ_(CO)^2 (k =1 h Mpc^(-1)) = 1.5_(-0.7}^(+0.7)} x 10^3 µK^2, at 68% confidence, and P_(CO) > 0 at 98.9% confidence. These results are a factor of 10 improvement in sensitivity compared to those of COPSS I. With this measurement, we constrain on the CO(1–0) galaxy luminosity function at z ~ 3. Assuming that CO emission is proportional to halo mass and using theoretical estimates of the scatter in this relationship, we constrain the ratio of CO(1-0) luminosity to halo mass to A_(CO) = 6.3_(-2.1)^(+1.4) x 10^(-7), L_⊙M_⊙^(-1). Assuming a Milky Way-like linear relationship between CO luminosity and molecular gas mass, we estimate a mass fraction of molecular gas of f_(H_2) = 5.5_(-2.2)^(+3.4) x 10^(-2) for halos with masses of ~10^(12) M_⊙. Using theoretical estimates for the scaling of molecular gas mass fraction and halo mass, we estimate the cosmic molecular gas density to be ρ_(z ~ 3)(H_2) = 1.1_(-0.4)^(+0.7) x 10^8 M_⊙ Mpc^(-3)