  Type Ia supernova (SN Ia) cosmology analyses include a luminosity step
function in their distance standardization process to account for an observed
yet unexplained difference in the post-standardization luminosities of SNe Ia
originating from different host galaxy populations (e.g., high-mass ($M \gtrsim
10^{10} M_{\odot}$) versus low-mass galaxies). We present a novel method for
including host-mass correlations in the SALT3 light curve model used for
standardising SN Ia distances. We split the SALT3 training sample according to
host-mass, training independent models for the low- and high-host-mass samples.
Our models indicate that there are different average Si II spectral feature
strengths between the two populations, and that the average SED of SNe from
low-mass galaxies is bluer than the high-mass counterpart. We then use our
trained models to perform a SN cosmology analysis on the 3-year
spectroscopically confirmed Dark Energy Survey SN sample, treating SNe from
low- and high-mass host galaxies as separate populations throughout. We find
that our mass-split models reduce the Hubble residual scatter in the sample,
albeit at a low statistical significance. We do find a reduction in the
mass-correlated luminosity step but conclude that this arises from the
model-dependent re-definition of the fiducial SN absolute magnitude rather than
the models themselves. Our results stress the importance of adopting a standard
definition of the SN parameters ($x_0, x_1, c$) in order to extract the most
value out of the light curve modelling tools that are currently available and
to correctly interpret results that are fit with different models.
