Alleviating the Hubble-constant tension and the growth tension via a transition of absolute magnitude favored by the Pantheon+ sample

Abstract: We establish a cosmological-model-independent method to extract the apparent magnitude and its derivative at different redshifts from the Pantheon+ type Ia supernova sample, and find that the obtained values deviate clearly from the prediction of the $\Lambda$CDM model at the lowest redshift. This deviation can be explained as a result of a transition of the absolute magnitude $M$ in the low redshift region. The observations seem to favor this transition since the minimum values of $\chi^2$ for two ansatzes of a varying $M$ are less than that of a constant $M$. The Hubble constant tension is alleviated from larger than $5\sigma$ to be about $1$ to $2\sigma$ for a varying $M$, and the growth tension can be resolved after attributing the variation of $M$ to a modification of the effective Newton's constant.