The measurements of the CMB temperature in diffuse interstellar medium of the Milky-Way and high redshift galaxies based on excitation of C_I fine-structure and H₂ rotational levels

Evolution of the cosmic microwave background (CMB) temperature with redshift ${T}_{\text{CMB}}={T}_{\text{CMB}}^{0}\times (1+z)$ is predicted by the standard ΛCDM cosmological model and has been confirmed by measurements of the Sunyaev-Zel'dovich effect in Plank data (at z ≤ 1) and excitation of CO rotational levels in quasar spectra (at 1.7 ≤ z ≤ 2.7). Excitation of the fine-structure levels of neutral carbon (C_I) is also sensitive to the temperature of the CMB radiation. However collisions and UV pumping lead to a significant degeneracy of the fitting parameters, since poor data on physical conditions. We found that a joint fit to excitation of low H₂ rotational and CI fine-structure levels can break this degeneracy and provide a tighter constraints on the T_CMB. We present estimates of the T_CMB derived from excitation of C_I fine-structure levels in the Milky Way clouds and high redshift absorption systems.