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 >4$\sigma$ disagreement between the local and high-redshift determinations of the Hubble constant, while maintaining the phenomenological success of the $\Lambda$CDM model with respect to the other observables. Here, we show that such a hockey-stick dark energy cannot solve the $H_0$ crisis. The basic reason is that the supernova absolute magnitude $M_B$ that is used to derive the local $H_0$ 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 $H_0$. 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 $q_0=-0.55$, 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 $H_0$ and $q_0$ that generalizes the prior on $H_0$ by SH0ES.

Overview of the Local Prior on the Absolute Magnitude of Type Ia Supernovae in Cosmological Inference

The paper by Camarena and Marra assesses the utility of employing the local prior on the absolute magnitude of Type Ia supernovae, denoted as ( M_B ), in cosmological inference, particularly in resolving the discrepancy between local and cosmological determinations of the Hubble constant ( H_0 ). The focus is a critical examination of whether adopting ( M_B ) has advantages over directly using prior constraints on ( H_0 ) for enhancing the precision and reliability of cosmological models.

In recent years, the tension between local measurements and cosmic microwave background (CMB) inference of ( H_0 ) in the context of the ΛCDM model has garnered significant attention. This tension potentially indicates a need for revisiting the standard cosmological model. One proposition to address this involves introducing a phenomenological model of dark energy that transitions to a phantom energy state at very low redshifts. This study demonstrates, using this model, that such a transition cannot reconcile the ( H_0 ) discrepancy when the analysis is attentive to the calibration of local supernovae.

The robustness of using ( M_B ) is analyzed through its application across various supernova datasets, and in conjunction with baryon acoustic oscillations (BAO) and CMB data. The authors argue that the calibration relating to ( M_B ) inherently incorporates essential local astrophysical information that is neglected when using ( H_0 ) priors.

Key Results and Methodological Considerations

1. Supernova Calibration Prior: The authors derive that adopting ( M_B ) prevents the double counting of low-redshift supernovae and avoids unnecessary assumptions of cosmographic models, thereby enabling unbiased parameter constraints and fair model comparison.

2. Statistical Performance: The analysis shows that models with abrupt exotic transitions in dark energy properties, such as the hockey-stick dark energy model, show no meaningful improvement when ( M_B ) calibration is correctly accounted for. When biased using ( H_0 ), inaccurate conclusions can result from neglecting ( M_B ).

3. Bayesian Marginalization: The paper provides statistical frameworks that retain the integrity of the dataset interpolations by ensuring proper marginalization of ( M_B ). The authors outline how ( M_B ) can be analytically marginalized without loss of generality, implying that ( M_B ) can be integrated into Bayesian inference straightforwardly.

Implications and Future Directions

This study's findings emphasize critical procedural refinements for analyzing dark energy models and the broader (\Lambda)CDM paradigm. In particular:

• Cosmological Model Testing: This work provides insight into refining constraints on new theories or models that aim to account for the observed ( H_0 ) tension. Future studies might focus on integrating varied local astrophysical data, such as host galaxy correlations, into supernova calibration procedures.

• Local Astrophysical Measurements: The interplay between local indices like ( M_B ) and cosmological parameters underlines the potential for more comprehensive approaches in modern cosmology that bridge local and high-redshift universe studies.

• Dark Energy Models: The restrictions presented by ( M_B ) clarify the limits of phantom dark energy transitions in resolving the ( H_0 ) crisis and suggest further work be directed towards exploring alternative models or engaging with modified gravity scenarios.

In conclusion, Camarena and Marra's study underscores the necessity of revisiting the fundamental assumptions underlying cosmological parameter estimation processes. Adopting ( M_B ) not only solidifies the statistical validity of cosmological analyses but also could significantly inform the ongoing refinement and testing of the standard model of cosmology.