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The Impact of Tomographic Redshift Bin Width Errors on Cosmological Probes

Systematic errors in the galaxy redshift distribution $n(z)$ can propagate to systematic errors in the derived cosmology. We characterize how the degenerate effects in tomographic bin widths and galaxy bias impart systematic errors on cosmology inference using observational data from the Deep Lens Survey. For this we use a combination of galaxy clustering and galaxy-galaxy lensing. We present two end-to-end analyses from the catalogue level to parameter estimation. We produce an initial cosmological inference using fiducial tomographic redshift bins derived from photometric redshifts, then compare this with a result where the redshift bins are empirically corrected using a set of spectroscopic redshifts. We find that the derived parameter $S_8 \equiv σ_8 (Ω_m/.3)^{1/2}$ goes from $.841^{+0.062}_{-.061}$ to $.739^{+.054}_{-.050}$ upon correcting the n(z) errors in the second method.