H0 tension or T0 tension? (Ivanov, Ali-Haïmoud, Lesgourgues)
We study whether the discrepancy between the local and cosmological measurements of the Hubble constant H0 can be reformulated as a tension in the cosmic microwave background (CMB) monopole temperature T0. The latter is customarily fixed to the COBE/FIRAS best-fit value in CMB anisotropy data analyses. We show that the primary CMB anisotropies and the shape of the matter power spectrum are not directly sensitive to T0. They depend only on the dark matter and baryon densities per CMB photon. Once these ratios are fixed, T0 only measures the time elapsed since recombination until today. This results is a nearly perfect geometric degeneracy between T0 and H0. Taken at face value, this implies that removing the FIRAS prior on T0 is enough to make the Planck CMB and SH0ES measurements consistent within the base ΛCDM model without introducing new physics. One may break the degeneracy by combining Planck with SH0ES, yielding an independent measurement of T0, which happens to be in a 4σ tension with FIRAS. Therefore, the Hubble tension can be fully recast into the T0 tension. The agreement with FIRAS can be restored if we combine Planck with the baryon acoustic oscillation data instead of SH0ES. Thus, the tension between SH0ES and cosmological measurements of H0 within ΛCDM persists even if we discard the FIRAS T0 measurement.