arXiv2026
The long-standing tension in the Hubble constant $H_0$ has motivated extensive explorations of both new physics and observational systematics, for example, the late-time systematics in measuring the B-band absolute magnitude $M_B$ of type Ia supernovae, which is degenerated with $H_0$ via an intercept $-5a_B=M_B+5\lg (c/H_0/\mathrm{Mpc})+25$ in the linear relation $m_B=5\lg d_L(z)-5a_B$ between the apparent magnitude $m_B$ and logarithmic dimensionless luminosity distance $\lg d_L(z)$. Therefore, this intercept can be evaluated directly from pure observational quantities ($m_B$ and the redshift $z$) for a given model of $d_L(z)$ without knowing underlying systematics in $M_B$-$H_0$ degeneracy. Hence, the constancy of this intercept across different supernova datasets and different redshift bins within the same dataset for a given late-time model serves as a powerful diagnostic for disentangling late-time new physics from local supernova systematics. In this mini-review, we will show that: (1) there is a local $a_B$ tension in PantheonPlus around $z\sim0.01$, and the elimination of it leads to a $H_0$ measurement consistent with both SH0ES typical three-rung and first two-rung measurements; (2) there is a late-time $a_B$ tension in DES-Y5 around $z\sim0.1$, and the elimination of it largely reduces the preference for dynamical dark energy. We also update the late-time $a_B$-tension analysis for both DES-Y5 and DES-Dovekie supernovae, and find that this $a_B$ tension around $z\sim0.1$ is mainly driven by the inter-data tension between DES supernovae and DESI+Planck constraint, and the dynamical dark energy is preferred as a compromise of this tension. Finally, we briefly mention an interacting dark energy model that resolves this tension among DES, DESI, and Planck, and point out a crucial difference between the effective and apparent equations of state of dark energy.