  Current and future cosmological analyses with Type Ia Supernovae (SNe Ia)
face three critical challenges: i) measuring redshifts from the supernova or
its host galaxy; ii) classifying SNe without spectra; and iii) accounting for
correlations between the properties of SNe Ia and their host galaxies. We
present here a novel approach that addresses each challenge. In the context of
the Dark Energy Survey (DES), we analyze a SNIa sample with host galaxies in
the redMaGiC galaxy catalog, a selection of Luminous Red Galaxies. Photo-$z$
estimates for these galaxies are expected to be accurate to $\sigma_{\Delta
z/(1+z)}\sim0.02$. The DES-5YR photometrically classified SNIa sample contains
approximately 1600 SNe and 125 of these SNe are in redMaGiC galaxies. We
demonstrate that redMaGiC galaxies almost exclusively host SNe Ia, reducing
concerns with classification uncertainties. With this subsample, we find
similar Hubble scatter (to within $\sim0.01$ mag) using photometric redshifts
in place of spectroscopic redshifts. With detailed simulations, we show the
bias due to using photo-$z$s from redMaGiC host galaxies on the measurement of
the dark energy equation-of-state $w$ is up to $\Delta w \sim 0.01-0.02$. With
real data, we measure a difference in $w$ when using redMaGiC photometric
redshifts versus spectroscopic redshifts of $\Delta w = 0.005$. Finally, we
discuss how SNe in redMaGiC galaxies appear to be a more standardizable
population due to a weaker relation between color and luminosity ($\beta$)
compared to the DES-3YR population by $\sim5\sigma$; this finding is consistent
with predictions that redMaGiC galaxies exhibit lower reddening ratios
($\textrm{R}_\textrm{V}$) than the general population of SN host galaxies.
These results establish the feasibility of performing redMaGiC SN cosmology
with photometric survey data in the absence of spectroscopic data.
