A doublet of cosmological models to challenge the H0 tension in the Pantheon Supernovae Ia catalog

$\Lambda$CDM provides a leading framework in the interpretation of modern cosmology. Nevertheless, the scientific community still struggles with many open problems in cosmology. Among the most noticeable ones, the tension in the Hubble constant $H_0$ is particularly intriguing, prompting a wide range of possible solutions. In the present work, the flat scale-free cosmology ($S$CDM) of Maeder (2017) is tested for $H_0$ tension in fits to the Pantheon sample of Supernovae Ia. The Pantheon sample is a collection of 1048 SNe Ia, which formally defines $H_0=H(0)$ by extrapolation to redshift zero of data over positive redshifts $z>0$. Here, we consider $H_{0,k}$ in fits of $S$CDM over $k$ equally sized bins of sub-samples of mean redshift $z_k$. To quantify a trend in $H_{0,k}$ with $z_k$, the results are fit by $f(z)=H'_0/(1+z)^\alpha$ in the two parameters $H'_0$ and $\alpha$. This approach tests for model imperfections or data biases by trends that are inconsistent with zero. Our findings show a decreasing trend inconsistent with zero at $5.3 \sigma$ significance, significantly more so than in $\Lambda$CDM. These results are further confirmed in Pantheon+. It appears that a solution to $H_0$ tension is to be found in models with a deceleration parameter $q_0<q_{0,\Lambda}$ below that of $\Lambda$CDM, rather than $q_{0,\Lambda} < q_{0,S}<0$ satisfied by $S$CDM.