Testing the Consistency of Dust Laws in SN Ia Host Galaxies: A BayeSN
  Examination of Foundation DR1
  We apply BayeSN, our new hierarchical Bayesian model for the SEDs of Type Ia
supernovae (SNe Ia), to analyse the $griz$ light curves of 157 nearby SNe Ia
($0.015<z<0.08$) from the public Foundation DR1 dataset. We train a new version
of BayeSN, continuous from 0.35--0.95 $\mu$m, which we use to model the
properties of SNe Ia in the rest-frame $z$-band, study the properties of dust
in their host galaxies, and construct a Hubble diagram of SN Ia distances
determined from full $griz$ light curves. Our $griz$ Hubble diagram has a low
total RMS of 0.13 mag using BayeSN, compared to 0.16 mag using SALT2.
Additionally, we test the consistency of the dust law $R_V$ between low- and
high-mass host galaxies by using our model to fit the full time- and
wavelength-dependent SEDs of SNe Ia up to moderate reddening (peak apparent
$B-V \lesssim 0.3$). Splitting the population at the median host mass, we find
$R_V=2.84\pm0.31$ in low-mass hosts, and $R_V=2.58\pm0.23$ in high-mass hosts,
both consistent with the global value of $R_V=2.61\pm0.21$ that we estimate for
the full sample. For all choices of mass split we consider, $R_V$ is consistent
across the step within $\lesssim1.2\sigma$. Modelling population distributions
of dust laws in low- and high-mass hosts, we find that both subsamples are
highly consistent with the full sample's population mean $\mu(R_V) =
2.70\pm0.25$ with a 95% upper bound on the population $\sigma(R_V) < 0.61$. The
$R_V$ population means are consistent within $\lesssim1.2\sigma$. We find that
simultaneous fitting of host-mass-dependent dust properties within our
hierarchical model does not account for the conventional mass step.
