Using Host Galaxy Photometric Redshifts to Improve Cosmological Constraints with Type Ia Supernova in the LSST Era

We perform a rigorous cosmology analysis on simulated type Ia supernovae (SN~Ia) and evaluate the improvement from including photometric host-galaxy redshifts compared to using only the "zspec" subset with spectroscopic redshifts from the host or SN. We use the Deep Drilling Fields (~50 deg^2) from the Photometric LSST Astronomical Time-Series Classification Challenge (PLaSTiCC), in combination with a low-z sample based on Data Challenge2 (DC2). The analysis includes light curve fitting to standardize the SN brightness, a high-statistics simulation to obtain a bias-corrected Hubble diagram, a statistical+systematics covariance matrix including calibration and photo-z uncertainties, and cosmology fitting with a prior from the cosmic microwave background. Compared to using the zspec subset, including events with SN+host photo-z results in i) more precise distances for z>0.5, ii) a Hubble diagram that extends 0.3 further in redshift, and iii) a 50 % increase in the Dark Energy Task Force figure of merit (FoM) based on the w0-wa CDM model. Analyzing 25 simulated data samples, the average bias on w0 and wa is consistent with zero. The host photo-z systematic of 0.01 reduces FoM by only 2 % because i) most z<0.5 events are in the zspec subset, ii) the combined SN+host photo-z has X 2 smaller bias, and iii) the anti-correlation between fitted redshift and color self corrects distance errors. To prepare for analysing real data, the next SNIa-cosmology analysis with photo-z's should include non SN-Ia contamination and host galaxy mis-associations.