Constraining R$_V$ Variation Using Highly Reddened Type Ia Supernovae from the Pantheon+ Sample

Type Ia supernovae (SNe Ia) are powerful tools for measuring the expansion history of the universe, but the impact of dust around SNe Ia remains unknown and is a critical systematic uncertainty. One way to improve our empirical description of dust is to analyse highly reddened SNe Ia ($E(B-V)>0.4$, roughly equivalent to the fitted SALT2 light-curve parameter $c>0.3$). With the recently released Pantheon+ sample, there are 57 SNe Ia that were removed because of their high colour alone (with colours up to $c=1.61$), which can provide enormous leverage on understanding line-of-sight $R_V$. Previous studies have claimed that $R_V$ decreases with redder colour, though it is unclear if this is due to limited statistics, selection effects, or an alternative explanation. To test this claim, we fit two separate colour-luminosity relationships, one for the main cosmological sample ($c<0.3$) and one for highly reddened ($c>0.3$) SNe Ia. We find the change in the colour-luminosity coefficient to be consistent with zero. Additionally, we compare the data to simulations with different colour models, and find that the data prefers a model with a flat dependence of $R_V$ on colour over a declining dependence. Finally, our results strongly support that line-of-sight $R_V$ to SNe Ia is not a single value, but forms a distribution.