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

Abstract

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 MB that is used to derive the local H0 constraint is not compatible with the MB 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 MB 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 MB 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 MB 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.

A buyer’s guide to the Hubble constant

“…A second problem with the use of H 0 priors has been discussed by Efstathiou (2021), who points out the difference between it and the actual data analysis performed by the SH0ES team, which is a calibration of the SN Ia fiducial absolute magnitude M B , followed by a conversion from M B to H 0 . To use an H 0 prior is then to transform and compress the data away from its true source; it would instead be better to use M B directly and priors for this are given in Camarena and Marra (2021). Another prevalent issue is the selective use of datasets-in particular, BAO provide strong constraints on the late universe as we shall see shortly, and to omit them is again to risk a misleading analysis.…”

On the Robustness of the Constancy of the Supernova Absolute Magnitude: Non-parametric Reconstruction \& Bayesian approaches

“…The possibility of a redshift variation in the absolute magnitude was suggested in Refs. [53,54] where they claim that the Hubble tension can also be reinterpreted through these variations in M B (z). Indeed, Refs.…”

“…In Refs. [54,100] it was argued that it is correct to use a prior on M B instead of a prior on H 0 . This is necessary to avoid double counting of low-redshift supernovae, and to avoid the deceleration parameter being set to the standard model value q 0 = −0.55, while accounting for M B being constrained by local calibration.…”

Observational constraints on the deceleration parameter in a tilted universe

“…where H 0 = 100h km sec −1 M pc −1 . Even though this degenerate combination is marginalized in most cases [9,76], recent studies [77][78][79][80] argue that this process may lead to physical information loss, since a physical model with an abrupt transition on the absolute magnitude M at a low redshift z t has the potential to alleviate simultaneously the H 0 and growth tensions [81][82][83][84][85][86][87][88]. Hence, we decide to use this degenerate parameter in the minimization process.…”