On the homogeneity of SnIa absolute magnitude in the Pantheon+ sample

We have analysed the Pantheon+ sample using a new likelihood model that replaces the single SnIa absolute magnitude parameter $M$ used in the standard likelihood model of Brout et. al. with two absolute magnitude parameters $M_<$, $M_>$ and a transition distance $d_{crit}$ that determines the distance at which $M$ changes from $M_<$ to $M_>$. The use of this likelihood dramatically changes the quality of fit to the Pantheon+ sample for a $\Lambda$CDM background by $\Delta \chi^2=-19.6$. The tension between the $M_<$ and $M_>$ best fit values is at a level more than $3\sigma$ with a best fit $d_{crit}$ very close to $20Mpc$. The origin of this improvement of fit and $M_<-M_>$ tension is that the new likelihood model, successfully models two signals hidden in the data: 1. The well known systematic effect called 'volumetric redshift scatter bias' which is due to asymmetric peculiar velocity variations at redshifts $z<0.01$ induced by unequal projected volumes at lower and higher distances compared to a given distance and 2. A mild signal for a change of intrinsic SnIa luminosity at about $20Mpc$. This interpretation of the results is confirmed by truncating the $z<0.01$ Hubble diagram data from Pantheon+ where the above systematic is dominant and showing that the $M_<-M_>$ tension decreases from above $3\sigma$ to a little less than $2\sigma$. It is also confirmed by a Monte Carlo simulation comparing the SnIa absolute luminosities $M_i$ of SnIa+Cepheid hosts, with the anticipated luminosities in the context of a homogeneous single absolute magnitude $M$. This simulation shows that the maximum significance of the SnIa luminosity transition ($\Sigma\equiv \frac{|M_>-M_<|}{\sqrt{\sigma_{M_>}^2+\sigma_{M_<}^2}}$) in the real data, is larger than the corresponding maximum significance of $94\%$ of the corresponding homogeneous simulated samples.