Effects of Redshift Uncertainty on Cross-Correlations of CMB Lensing and Galaxy Surveys

Understand

We explore the effects of incorporating redshift uncertainty into measurements of galaxy clustering and cross-correlations of galaxy positions and cosmic microwave background (CMB) lensing maps.

• We use a simple Gaussian model for a redshift distribution in a redshift bin with two parameters: the mean, $z_0$, and the width, $\sigma_z$.
• We vary these parameters, as well as a galaxy bias parameter, $b_{\text{g}}$, and a matter fluctuations parameter, $\sigma_8$, for each redshift bin, as well as the parameter $\Omega_{\text{m}}$, in a Fisher analysis across 12 redshift bins from $z=0-7$.
• We find that incorporating redshift uncertainties degrades constraints on $\sigma_8(z)$ in the Large Synoptic Survey Telescope (LSST)/CMB-S4 era by about a factor of 10 compared to the case of perfect redshift knowledge.