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 $zsim1.2$ 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.
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