The impact of spectroscopic redshift errors on cosmological measurements

Spectroscopic redshift errors, including redshift uncertainty and catastrophic failures, can bias cosmological measurements from galaxy clustering at sub-percent level. In this work, we investigate their impact on the full-shape analysis using contaminated mock catalogs. We find that redshift uncertainty introduces a scale-dependent damping effect on the power spectrum, which is absorbed by counterterms in clustering model, keeping parameter biases below 5%. Catastrophic failures suppress the power spectrum amplitude by an approximately constant factor, which scales with the catastrophic rate fc. While this effect is negligible for DESI galaxy populations (fc = 1%), the slitless-like errors, combining redshift uncertainty with fc = 5% catastrophics, introduce significant biases in cosmological constraints. In this case, we find 6% to 16% shifts (similar to 2.2 sigma level) in estimating the fractional growth rate df equivalent to f /ffid and the log primordial amplitude ln(1010As). Applying the correction factor (1-fc)2 on the galaxy power spectrum mitigates the bias but weakens the parameter constraints due to new degeneracies. Alternatively, fixing fc to its expected value restores the constraining power with a modest bias of 1.0 sigma. Our results indicate that for space-based slitless surveys such as Euclid, at minimum accurate estimation of fc and its incorporation into the clustering model are necessary to get unbiased cosmological inference. Extending to evolving dark energy and massive neutrino cosmologies, redshift errors do not bias the dark energy properties parametrized by w0 and wa, but can degrade constraints on the summed neutrino mass m nu by up to 80% in the worst case.