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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 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.

The determination of the Hubble constant H 0 from the cosmic microwave background by the Planck Collaboration (N. Aghanim et al., arXiv:1807.06209) is in tension at 4.2σ with respect to the local determination of H 0 by the SH0ES collaboration [M. J. Reid et al., Astrophys. J. Lett. 886, L27 (2019)]. Here we improve upon the local determination, which fixes the deceleration parameter to the standard CDM model value of q 0 = −0.55, that is, uses information from observations beyond the local universe. First, we derive the effective calibration prior on the absolute magnitude M B of type Ia supernovae, which can be used in cosmological analyses in order to avoid the double counting of low-redshift supernovae. We find M B = −19.2334 ± 0.0404 mag. Then we use the above M B prior in order to obtain a determination of the local H 0 which uses only local observations and assumes only the cosmological principle, that is, large-scale homogeneity and isotropy. This is achieved by adopting an uninformative flat prior for q 0 in the cosmographic expansion of the luminosity distance. We use the latest Pantheon sample and find H 0 = 75.35 ± 1.68 km s −1 Mpc −1 , which features a 2.2% uncertainty, close to the 1.9% error obtained by the SH0ES Collaboration. Our determination is at the higher tension of 4.5σ with the latest results from the Planck Collaboration that assume the CDM model. Furthermore, we also constrain the deceleration parameter to q 0 = −1.08 ± 0.29, which disagrees with the Planck Collaboration at the 1.9σ level. These estimations only use supernovae in the redshift range 0.023 z 0.15.

The current 3.8σ tension between local [1] and global [2] measurements of H0 cannot be fully explained by the concordance ΛCDM model. It could be produced by unknown systematics or by physics beyond the standard model. In particular, non-standard dark energy models were shown to be able to alleviate this tension. On the other hand, it is well known that linear perturbation theory predicts a cosmic variance on the Hubble parameter H0, which leads to systematic errors on its local determination. Here, we study how including in the likelihood the cosmic variance on H0 affects statistical inference. In particular we consider the γCDM, wCDM and γwCDM parametric extensions of the standard model, which we constrain with the latest CMB, BAO, SNe Ia, RSD and H0 data. We learn two important lessons. First, the systematic error from cosmic variance is -independently of the model -approximately σcv ≈ 0.88 km s −1 Mpc −1 (1.2% H loc 0 ) when considering the redshift range 0.0233 ≤ z ≤ 0.15, which is relative to the main analysis of [1], and σcv ≈ 1.5 km s −1 Mpc −1 (2.1% H loc 0 ) when considering the wider redshift range 0.01 ≤ z ≤ 0.15. Although σcv affects the total error budget on local H0, it does not significantly alleviate the tension which remains at ≈ 3σ. Second, cosmic variance, besides shifting the constraints, can change the results of model selection: much of the statistical advantage of non-standard models is to alleviate the now-reduced tension. We conclude that, when constraining non-standard models it is important to include the cosmic variance on H0 if one wants to use the local determination of the Hubble constant by Riess et al. [1]. Doing the contrary could potentially bias the conclusions.