Late-transition versus smooth H(z)-deformation models for the resolution of the Hubble crisis

Gravitational transitions at low redshifts (zt < 0.1) have been recently proposed as a solution to the Hubble and growth tensions. Such transitions would naturally lead to a transition in the absolute magnitude M of type Ia supernovae (SnIa) at zt (Late M Transitions - LMT) and possibly in the dark energy equation of state parameter w (Late w − M Transitions - LwMT). Here, we compare the quality of fit of this class of models to cosmological data, with the corresponding quality of fit of the cosmological constant model (ΛCDM) and some of the best smooth H(z) deformation models (wCDM, CPL, PEDE). We also perform model selection via the Akaike Information Criterion and the Bayes factor. We use the full CMB temperature anisotropy spectrum data, the baryon acoustic oscillations (BAO) data, the Pantheon SnIa data, the SnIa absolute magnitude M as determined by Cepheid calibrators and the value of the Hubble constant H0 as determined by local SnIa calibrated using Cepheids. We find that smooth H(z) deformation models perform worse than transition models for the following reasons: 1) They have a worse fit to low-z geometric probes (BAO and SnIa data); 2) They favor values of the SnIa absolute magnitude M that are lower as compared to the value Mc obtained with local Cepheid calibrators at z < 0.01; 3) They tend to worsen the Ωm,0−σ8,0 growth tension. We also find that the w−M transition model (LwMT) does not provide a better quality of fit to cosmological data than a pure M transition model (LMT) where w is fixed to the ΛCDM value w = −1 at all redshifts. We conclude that the LMT model has significant statistical advantages over smooth late-time H(z) deformation models in addressing the Hubble crisis.