Gravitational transitions at low redshifts ($z_t<0.1$) 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 $z_t$ (late $M$ transitions—$LMT$) and possibly in the dark energy equation of state parameter $w$ (late $w-M$ transitions). 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 ($\mathrm{\Lambda }\mathrm{CDM}$) and some of the best smooth $H(z)$ deformation models [$w\mathrm{CDM}$ (cold dark matter), Chevallier-Polarski-Linder, phenomenologically emergent dark energy]. We also perform model selection via the Akaike information criterion (AIC) and the Bayes factor. We use the full cosmic microwave background temperature anisotropy spectrum data, the baryon acoustic oscillations data, the Pantheon SNIa data, the SNIa absolute magnitude $M$ as determined by Cepheid calibrators and the value of the Hubble constant $H_0$ 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 (baryon acoustic oscillations and SNIa data); (2) they favor values of the SNIa absolute magnitude $M$ that are lower as compared to the value $M_c$ obtained with local Cepheid calibrators at $z<0.01$; (3) They tend to worsen the ${\mathrm{\Omega }}_{\mathrm{m},0}-{\sigma }_{8,0}$ growth tension. We also find that the $w-M$ transition model does not provide a better quality of fit to cosmological data than a pure $M$ transition model ($LMT$), where $w$ is fixed to the $\mathrm{\Lambda }\mathrm{CDM}$ 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.

• Received 19 October 2021
• Accepted 25 February 2022

DOI:https://doi.org/10.1103/PhysRevD.105.063538