Scale invariant cosmology and CMB temperatures as a function of redshifts

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, Omega_Lambda vs. Omega_m plot, age vs. H_0, H(z) vs. z, transition braking-acceleration) have indicated an impressive agreement {Maeder 2017}. 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/H_2) 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) vs.z. Thus, the agreement often found with the standard model may be questioned. The T(CMB)vs. z relation needs further careful attention and the same for the scale invariant cosmology in view of its positive tests.