The Pantheon+ Analysis: Forward-Modeling the Dust and Intrinsic Colour Distributions of Type Ia Supernovae, and Quantifying their Impact on Cosmological Inferences

Recent studies have shown that the observed colour distributions of Type Ia SNe (SNIa) are well-described by a combination of distributions from dust and intrinsic colour. Here we present a new forward-modeling fitting method (Dust2Dust) to measure the parent dust and colour distributions, including their dependence on host-galaxy mass. At each fit step, the SNIa selection efficiency is determined from a large simulated sample that is re-weighted to reflect the proposed distributions. We use five separate metrics to constrain the Dust2Dust parameters: distribution of fitted light-curve colour $c$, cosmological residual trends with $c$, cosmological residual scatter with $c$, fitted colour-luminosity relationship $\beta_{\rm SALT2}$, and intrinsic scatter $\sigma_{\rm int}$. Using the Pantheon+ data sample, we present results for a Dust2Dust fit that includes 4 parameters describing intrinsic colour variations and 8 parameters describing dust. Furthermore, we propagate the Dust2Dust parameter uncertainties and covariance to the dark energy equation-of-state $w$ and Hubble constant H$_0$: we find $\sigma_w = 0.005$ and $\sigma_{\textrm{H}_0} = 0.145~$km/s/Mpc. The Dust2Dust code is publically available.