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On the use of the local prior on the absolute magnitude of Type Ia supernovae in cosmological inference
David Camarena, Valerio Marra
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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 ΛCDM 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, BAO and CMB 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 SH0ES.
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