A Comparative Study of the Ground State Transitions of CO and C <sc>i</sc> as Molecular Gas Tracers at High Redshift

The CO(1-0) and [C i](1-0) emission lines are well-established tracers of cold molecular gas mass in local galaxies. At high redshift, where the interstellar medium is likely to be denser, there have been limited direct comparisons of both ground-state transitions. We present a comparison of [C i](1-0) and CO(1-0) emission in 20 unlensed dusty, star-forming galaxies at z >= 2-5. The CO(1-0)/[C i](1-0) ratio remains constant up to z = 5, supporting the reliability of [C i](1-0) as a gas-mass tracer. We use the CO(1-0), [C i](1-0), and 3 mm dust continuum measurements to cross-calibrate their respective gas mass conversion factors, finding no dependence of these factors on either redshift or infrared luminosity. Radiative transfer modeling shows that the warmer cosmic microwave background (CMB) at high redshift can significantly affect the [C i] as well as CO emission, which can change the derived molecular gas masses by up to 70% for the coldest kinetic gas temperatures expected. Nevertheless, the magnitude of the CMB effect on the CO/[C i] ratio is within the known scatter of the LCO '-L[CI]' relation. Precisely determining the CMB effect on individual line intensities would require well-sampled spectral line energy distributions to robustly model the gas excitation conditions. Finally, we note that adopting a variable CO gas-mass conversion factor for different galaxy populations implies [C i](1-0) and dust conversion factors that differ from canonically assumed values. However, the revised conversion factors are consistent with expectations for (super)solar metallicities likely to be found in high-redshift dusty galaxies.