On the use of the local prior on the absolute magnitude of Type Ia supernovae in cosmological inference

A dark-energy, which behaves as the cosmological constant until a sudden phantom transition at very low redshift (z < 0.1), seems to solve the >4σ disagreement between the local and high-redshift determinations of the Hubble constant, while maintaining the phenomenological success of the Λ cold dark matter model with respect to the other observables. Here, we show that such a hockey-stick dark energy cannot solve the H₀ crisis. The basic reason is that the supernova absolute magnitude M_B that is used to derive the local H₀ constraint is not compatible with the M_B that is necessary to fit supernova, baryon acoustic oscillation, and cosmic microwave background data, and this disagreement is not solved by a sudden phantom transition at very low redshift. We make use of this example to show why it is preferable to adopt in the statistical analyses the prior on M_B as an alternative to the prior on H₀. The three reasons are: (i) one avoids potential double counting of low-redshift supernovae, (ii) one avoids assuming the validity of cosmography, in particular, fixing the deceleration parameter to the standard model value q₀ = -0.55, (iii) one includes in the analysis the fact that M_B is constrained by local calibration, an information which would otherwise be neglected in the analysis, biasing both model selection and parameter constraints. We provide the priors on M_B relative to the recent Pantheon and DES-SN3YR supernova catalogs. We also provide a Gaussian joint prior on H₀ and q₀ that generalizes the prior on H₀ by Supernova H0 for the Equation of State.