A Simulation Based Inference Approach to Modelling of Type Ia Supernova Populations
Type Ia Supernovae (SNe Ia) are prominent cosmological probes, utilising a standardisation process to reduce their observed scatter to $\sim0.15$ mag. A growing number of models seek to explain this remaining intrinsic scatter, based on a diversity of dust properties and possible connections to the progenitor systems. Inference of new models has been limited due to the cost of simulations and attendant complexity. Here, we present Stj\"ornum\'al, a simulation based inference pipeline to infer intrinsic and extrinsic parameters of SNe Ia, an upgrade to previous SN Ia modelling attempts with SALT, e.g. Dust2Dust. Stj\"ornum\'al provides fast and accurate posterior inference via Neural Posterior Estimation, integrated model comparison with Neural Ratio Estimation, and overall significant speed and quality-of-life upgrades. We fit the Dark Energy Survey (DES) 5-year SN sample, finding good agreement with previously-published dust model parameters for DES5YR. We test 7 models of SN Ia behaviour, finding that more data is needed to break degeneracies between $R_V$ models, but sufficient to evidence ($\log(10)~\textrm{Bayes Factor} = +1.9$, $f_{\rm mix} = 0.8$) against two populations of SNe Ia at high-redshift. We employ a combination of frequentist $\chi^2$ metrics and Bayesian model comparison to make model determinations, finding neither are sufficient on their own to properly compare models. For our nominal model, we find a smaller $\Delta R_V = 0.8$ for our nominal model than previous SALT-based attempts. We test our model for consistency against our assumed cosmology, and find our results are robust to $|\Delta w| < 0.10$. The code is publicly available at https://github.com/bap37/Stjornumal, and presents an opportunity to flexibly and rapidly test potential models of SNe Ia scatter in a common framework.