  During the first several days after explosion, Type Ia supernova light curves
probe the outer layers of the exploding star and therefore provide important
clues for identifying their progenitors. We investigate how both the shallow
$^{56}$Ni distribution and the presence of circumstellar material shape these
early light curves. This is performed using a series of numerical experiments
with parameterized properties for systematic exploration. Although not all of
the considered models may be realized in nature (and indeed there are arguments
why some of them should not occur), the spirit of this work is to provide a
broader exploration of the diversity of possibilities. We find that shallower
$^{56}$Ni leads to steeper, bluer light curves. Differences in the shape of the
rise can introduce errors in estimating the explosion time and thus impact
efforts to infer upper limits on the progenitor or companion radius from a lack
of observed shock cooling emission. Circumstellar material can lead to
significant luminosity during the first few days, but its presence can be
difficult to identify depending on the degree of nickel mixing. In some cases,
the hot emission of circumstellar material may even lead to a signature similar
to interaction with a companion, and thus in the future additional diagnostics
should be gathered for properly assessing early light curves.
