Non-Gaussian Likelihoods for Type Ia Supernovae Cosmology: Implications for Dark Energy and $H_0$

The latest improvements in the scale and calibration of Type Ia supernovae catalogues allow us to constrain the specific nature and evolution of dark energy through its effect on the expansion history of the universe. We present the results of Bayesian cosmological model comparison on the SNe~Ia catalogue Pantheon+, where Flat $\Lambda$CDM is preferred by the data over all other models and we find moderate evidence ($\Delta \log \mathcal{Z} \sim 2.5$) to reject a number of the alternate dark energy models. The effect of peculiar velocity corrections on model comparison is analysed, where we show that removing the peculiar velocity corrections results in a varying fit on non-$\Lambda$CDM parameters. As well as comparing cosmological models, the Bayesian methodology is extended to comparing the scatter model of the data, testing for non-gaussianity in the Pantheon+ Hubble residuals. We find that adding a scale parameter to the Pantheon+ covariances, or alternately using a multivariate Student's t-distribution fits the data better than the fiducial analysis, producing a cosmology independent evidence increase of $\Delta \log \mathcal{Z} = 2.29$ and $2.46$ respectively. This improved treatment of the scatter decreases the uncertainty in the constraint on the Hubble constant, finding $H_0 = 73.67 \pm 0.99$ km s$^{-1}$ Mpc$^{-1}$, in $5.7 \sigma$ tension with Planck. We also explore $M_B$ transition models as a potential solution for the Hubble tension, finding no evidence to support these models among the SNe data.