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.
