We present results of analysis of physical conditions (number density, intensity of UV field, kinetic temperature) in the cold H$_2$-bearing interstellar medium of local and high redshift galaxies. Our measurements based on the fit to the observed population of H$_2$ rotational levels and CI fine-structure levels with the help of grids of numerical models calculated with the PDR Meudon code. A joint analysis of low H$_2$ rotational levels and CI fine-structure levels allows to break the degeneracy in the $I_{UV}-n_{rm{H}}$ plane and provides significantly tighter constraints on the number density and intensity of UV field. Using archive data from the VLT/UVES, KECK/HIRES, HST/STIS and FUSE telescopes we selected 12 high redshift damped Ly$alpha$ systems (DLAs) in quasar spectra and 14 H$_2$ absorption systems along the lines of sight towards stars in the Milky-Way and the Magellanic Clouds galaxies. These systems have strong H$_2$ components with the column density $log N({rm{H_2}})/{rm{cm}}^{-2}>18$ and associated CI absorptions. We find that H$_2$-bearing medium in high redshift DLAs and in local galaxies has similar values of the kinetic temperatures $T_{rm{kin}}sim100$K and number density $10-500$ cm$^{-3}$. However, the intensity of incident UV radiation in DLAs is varied in the wide range ($0.1-100$ units of Mathis field), while it is $sim0.1-3$ units of Mathis field for H$_2$ systems in Milky-Way and LMC and SMC galaxies. The large dispersion of measured UV flux in DLAs is probably a consequence that DLA sample probes the galaxies selected from the overall galaxy population at high-z and therefore corresponds to the wide range of the physical conditions.
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