Estimation of the CMB temperature from atomic C\,{\sc i} and molecular CO lines in the interstellar medium of early galaxies

Abstract

The linear increase of the cosmic microwave background (CMB) temperature with cosmological redshift, $T_{\mathrm{CMB}}=T_0(1+z)$, is a prediction of the standard cosmological $\Lambda$CDM model. There are currently two methods to measure this dependence at redshift $z>0$, and that is equally important to estimate the CMB temperature $T_0$ at the present epoch $z=0$. The first method is based on the Sunyaev-Zeldovich (SZ) effect for a galaxy cluster. aThe second method is based on the analysis of the populations of atomic and molecular energy levels observed in the absorption spectra of quasars. This method allows $T_{\mathrm{CMB}}(z)$ to be measured directly. We present new estimates of $T_{\mathrm{CMB}}(z_i)$ in the redshift range $1.7\le z_i\le 3.3$ based on the analysis of excitation of the CO rotational levels and C\,{\sc i} fine-structure levels in 15 absorption systems. We take into account collisional excitation of CO and C\,{\sc i} with hydrogen atoms and H${}_2$ and radiative pumping of C\,{\sc i} by the interstellar ultraviolet radiation. Applying this corrections leads to a systematic decrease in the previously obtained estimates of $T_{\mathrm{CMB}}(z_i)$ (for some systems the magnitude of the effect is $\sim$10\%). Combining our measurements with the measurements of $T_{\mathrm{CMB}}(z)$ in galaxy clusters we have obtained a constraint on the parameter $\beta =+0.010\pm 0.013$, which characterizes the deviation of the CMB temperature from the standard relation, $T_{\mathrm{CMB}}=T_0(1+z{)}^{1-\beta }$, and an independent estimate of the CMB temperature at the present epoch, $T_0=2.719\pm 0.009$\,K, which agrees well with the estimate from orbital measurements, $T_0=2.7255\pm 0.0006$\,K. This independent estimate is very important because it was obtained using cosmological data, in contrast to satellite measurements, which are obtained "here" and "now".

8 pages, 4 figures, 5 tables

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• Revisiting the temperature evolution law of the CMB with gaussian processes
• Lorentzian correction for the evolution of the CMB temperature
• Cosmology with the SZ spectrum: measuring the Universe's temperature with galaxy clusters
• Cosmic microwave background temperature cosmography