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We present a survey for neutral atomic-carbon (CI) along gamma-ray burst(GRB) sightlines, which probes the shielded neutral gas-phase in theinterstellar medium (ISM) of GRB host galaxies at high redshift. We compile asample of 29 medium- to high-resolution GRB optical afterglow spectra spanninga redshift range through most of cosmic time from $1 < z < 6$. We find thatseven ($\approx 25\%$) of the GRBs entering our statistical sample have CIdetected in absorption. It is evident that there is a strong excess of cold gasin GRB hosts compared to absorbers in quasar sightlines. We investigate thedust properties of the GRB CI absorbers and find that the amount of neutralcarbon is positively correlated with the visual extinction, $A_V$, and thestrength of the 2175 \AA\ dust extinction feature, $A_{\mathrm{bump}}$. GRBswith CI detected in absorption are all observed above a certain threshold of$\log N$(HI)$/\mathrm{cm}^{-2}$ + [X/H] > 20.7 and a dust-phase iron columndensity of $\log N$(Fe)$_{\mathrm{dust}}/\mathrm{cm}^{-2}$ > 16.2. In contrastto the SED-derived dust properties, the strength of the CI absorption does notcorrelate with the depletion-derived dust properties. This indicates that theGRB CI absorbers trace dusty systems where the dust composition is dominated bycarbon-rich dust grains. The observed higher metal and dust column densities ofthe GRB CI absorbers compared to H$_2$- and CI-bearing quasar absorbers ismainly a consequence of how the two absorber populations are selected, but isalso required in the presence of intense UV radiation fields in activelystar-forming galaxies.

Cold gas in the early Universe. Survey for neutral atomic-carbon in GRB host galaxies at 1 < z < 6 from optical afterglow spectroscopy