2017ApJ...847...65M

Cosmological models assuming the scale invariance of the macroscopic empty space show an accelerated expansion, without calling for some unknown particles. Several comparisons between models and observations (tests on distances, m-z diagram, Ω_Λ versus Ω_m plot, age versus H₀, H(z) versus z, transition braking-acceleration) have indicated an impressive agreement. We pursue the tests with the CMB temperatures T_CMB as a function of redshifts z. CO molecules in DLA systems provide the most accurate excitation temperatures T_exc up to z~2.7. Such data need corrections for local effects like particle collisions, optical depths, UV radiation, etc., We estimate these corrections as a function of the (CO/H₂) ratios from far-UV observations of CO molecules in the Galaxy. The results show that it is not sufficient to apply theoretical collisional corrections to get the proper values of T_CMB versus z. Thus, the agreement often found with the standard model may be questioned. The T_CMB(z) relation needs further careful attention and the same for the scale-invariant cosmology in view of its positive tests.