The effects of varying colour-luminosity relations on supernova science
  The success of Type Ia supernova (SN Ia) distance standardisation for
cosmology relies on a single global linear relationship between their peak
luminosity and colour, the $\beta$ parameter. However, there are several pieces
of evidence and physical reasons to believe that this relation is not universal
and may change within different subgroups, or even among individual objects. In
this work, we allow $\beta$ to vary among subpopulations with different
observed properties in the cosmological fits. Although the inferred
cosmological parameters are consistent with previous studies that assume a
single colour-luminosity relation, we find that the SN data favour nonuniversal
distributions of $\beta$ when split according to SN colour and/or host-galaxy
mass. For galaxy mass, we obtain a $\beta$-step relation in which low $\beta$
values occur in more massive galaxies, a trend that can be explained by
differing dust reddening laws for two types of environments. For colour, we
find that bluer/redder SNe Ia are consistent with a lower/larger $\beta$. This
trend is explained with $\beta$ being a combination of a low intrinsic
colour-luminosity relation dominant in bluer SNe and a higher extrinsic
reddening relation dominant at redder colours. The host galaxy mass-step
correction always provides better distance calibration, regardless of the
multiple $\beta$ approaches, and we suggest that it may come from a difference
in intrinsic colour-luminosity properties of SNe Ia in two types of
environments. Additionally, we find that blue SNe in low-mass environments are
better standard candles than the others.
