  Type Ia supernovae (SNe Ia) play a crucial role as standardizable candles in
measurements of the Hubble constant and dark energy. Increasing evidence points
towards multiple possible explosion channels as the origin of normal SNe Ia,
with possible systematic effects on the determination of cosmological
parameters. We present, for the first time, a comprehensive comparison of
publicly-available SN Ia model nucleosynthetic data with observations of
late-time light curve observations of SN Ia events. These models span a wide
range of white dwarf (WD) progenitor masses, metallicities, explosion channels,
and numerical methodologies. We focus on the influence of $^{57}$Ni and its
isobaric decay product $^{57}$Co in powering the late-time ($t > 1000$ d) light
curves of SNe Ia. $^{57}$Ni and $^{57}$Co are neutron-rich relative to the more
abundant radioisotope $^{56}$Ni, and are consequently a sensitive probe of
neutronization at the higher densities of near-Chandrashekhar (near-$M_{\rm
Ch}$) progenitor WDs. We demonstrate that observations of one SN Ia event, SN
2015F is only consistent with a sub-$M_{\rm Ch}$ WD progenitor. Observations of
four other events (SN 2011fe, SN 2012cg, SN 2014J, SN2013aa) are consistent
with both near-$M_{\rm Ch}$ and sub-$M_{\rm Ch}$ progenitors. Continued
observations of late-time light curves of nearby SNe Ia will provide crucial
information on the nature of the SN Ia progenitors.
