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

TL;DR

This paper refines measurements of the CMB temperature at high redshifts using atomic and molecular absorption lines, providing an independent estimate of the present-day CMB temperature consistent with satellite data.

Contribution

It introduces improved estimates of the CMB temperature at redshifts 1.7 to 3.3 by accounting for collisional and radiative effects, and combines these with cluster data to constrain deviations from standard cosmology.

Findings

Estimated T_CMB(z) at 1.7 ≤ z ≤ 3.3 with corrections for collisional excitation.

Derived T_0 = 2.719 ± 0.009 K for the present-day CMB temperature.

Found no significant deviation from the standard T_CMB = T_0(1+z) relation.

Abstract

The linear increase of the cosmic microwave background (CMB) temperature with cosmological redshift, $T_{\rm CMB} = T_0(1 + z)$, 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 $T_{\rm CMB}(z)$ to be measured directly. We present new estimates of $T_{\rm CMB}(z_i)$ in the redshift range $1.7\le z_i \le3.3$ 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 $T_{\rm CMB}(z_i)$ (for some systems the magnitude of the effect is $\sim$10\%). Combining our measurements with the measurements of $T_{\rm CMB}(z)$ in galaxy clusters we have obtained a constraint on the parameter $\beta=+0.010\pm0.013$, which characterizes the deviation of the CMB temperature from the standard relation, $T_{\rm CMB} = T_0(1 + z)^{1-\beta}$, and an independent estimate of the CMB temperature at the present epoch, $T_0 = 2.719\pm0.009$\,K, which agrees well with the estimate from orbital measurements, $T_0 = 2.7255\pm0.0006$\,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".