A precise and accurate determination of the cosmic microwave background temperature at z=0.89

Context. According to the Big Bang theory and as a consequence of adiabatic expansion of the Universe, the temperature of the cosmic microwave background (CMB) increases linearly with redshift. This relation is, however, poorly explored, and detection of any deviation would directly lead to (astro-)physics beyond the standard model. Aims. We aim to measure the temperature of the CMB with an accuracy of a few percent at z = 0.89 toward the molecular absorber in the galaxy lensing the quasar PKS 1830-211. Methods. We adopted a Monte-Carlo Markov chain approach, coupled with predictions from the non-LTE radiative transfer code RADEX, to solve the excitation conditions of a set of various molecular species directly from their spectra. Results. We determine T-CMB = 5.08 +/- 0.10 K at 68% confidence level. Our measurement is consistent with the value T-CMB = 5.14 K predicted by the standard cosmological model with adiabatic expansion of the Universe. This is the most precise determination of T-CMB at z > 0 to date.