On Redshift Evolution & Negative Dark Energy Density in Pantheon+ Supernovae

Within the Friedmann-Lema\^itre-Robertson-Walker (FLRW) framework, the Hubble constant $H_0$ is an integration constant. Thus, consistency of the model demands observational constancy of $H_0$. We demonstrate redshift evolution of best fit $\Lambda$CDM parameters $(H_0, \Omega_{m})$ in Pantheon+ supernove (SNe). Redshift evolution of best fit cosmological parameters is a prerequisite to finding a statistically significant evolution as well as identifying alternative models that are competitive with $\Lambda$CDM in a Bayesian model comparison. To assess statistical significance, we employ three different methods: i) Bayesian model comparison, ii) mock simulations and iii) profile distributions. The first shows a marginal preference for the vanilla $\Lambda$CDM model over an ad hoc model with 3 additional parameters and an unphysical jump in cosmological parameters at $z=1$. From mock simulations, we estimate the statistical significance of redshift evolution of best fit parameters and negative dark energy density ($\Omega_m > 1$) to be in the $1-2 \sigma$ range, depending on the criteria employed. Importantly, in direct comparison to the same analysis with the earlier Pantheon sample we find that statistical significance of redshift evolution of best fit parameters has increased, as expected for a physical effect. Our profile distribution analysis demonstrates a shift in $(H_0, \Omega_m)$ in excess of $95\%$ confidence level for SNe with redshifts $z > 1$ and also shows that a degeneracy in MCMC posteriors is not equivalent to a curve of constant $\chi^2$. Our findings can be interpreted as a statistical fluctuation or unexplored systematics in Pantheon+ or $\Lambda$CDM model breakdown. The first two possibilities are disfavoured by similar trends in independent probes.