  We present the first results of an ALMA survey of the lower fine structure
line of atomic carbon [C I]$(^3P_1\,-\,^{3}P_0)$ in far infrared-selected
galaxies on the main sequence at $z\sim1.2$ in the COSMOS field. We compare our
sample with a comprehensive compilation of data available in the literature for
local and high-redshift starbursting systems and quasars. We show that the [C
I]($^3P_1$$\rightarrow$$^3P_0$) luminosity correlates on global scales with the
infrared luminosity $L_{\rm IR}$ similarly to low-$J$ CO transitions. We report
a systematic variation of $L'_{\rm [C\,I]^3P_1\,-\, ^3P_0}$/$L_{\rm IR}$ as a
function of the galaxy type, with the ratio being larger for main-sequence
galaxies than for starbursts and sub-millimeter galaxies at fixed $L_{\rm IR}$.
The $L'_{\rm [C\,I]^3P_1\,-\, ^3P_0}$/$L'_{\rm CO(2-1)}$ and $M_{\rm{[C
I]}}$/$M_{\rm dust}$ mass ratios are similar for main-sequence galaxies and for
local and high-redshift starbursts within a 0.2 dex intrinsic scatter,
suggesting that [C I] is a good tracer of molecular gas mass as CO and dust. We
derive a fraction of $f_{\rm{[C\,I]}} = M_{\rm{[C\,I]}} / M_{\rm{C}}\sim3-13$%
of the total carbon mass in the atomic neutral phase. Moreover, we estimate the
neutral atomic carbon abundance, the fundamental ingredient to calibrate [C I]
as a gas tracer, by comparing $L'_{\rm [C\,I]^3P_1\,-\, ^3P_0}$ and available
gas masses from CO lines and dust emission. We find lower [C I] abundances in
main-sequence galaxies than in starbursting systems and sub-millimeter
galaxies, as a consequence of the canonical $\alpha_{\rm CO}$ and gas-to-dust
conversion factors. This argues against the application to different galaxy
populations of a universal standard [C I] abundance derived from highly biased
samples.
