The Impact of Spectroscopic Redshift Errors on Cosmological Measurements

TL;DR

This work quantifies how spectroscopic redshift errors, including small redshift uncertainties and catastrophic failures, bias full-shape cosmological inferences from galaxy clustering. Using 500 contaminated Quijote mocks, it shows redshift uncertainty induces scale-dependent damping that EFT counterterms can absorb, while redshift catastrophics suppress the power spectrum by a factor roughly $(1-f_c)^2$. For DESI-like regimes, catastrophics are negligible, but slitless-like Euclid-like errors can bias key parameters; correcting with $(1-f_c)^2$ or by marginalizing over $f_c$ mitigates bias but can degrade constraints. Extending to evolving dark energy and massive neutrinos, redshift errors do not bias $w_0$ or $w_a$ but can significantly weaken $\sum m_\nu$ constraints, particularly for high $f_c$ scenarios. The results emphasize that accurate modeling of redshift-error rates, especially in space-based slitless surveys, is crucial for unbiased cosmology, while BAO remains robust to these systematics.

Abstract

Spectroscopic redshift errors, including redshift uncertainty and catastrophic failures, can bias cosmological measurements from galaxy redshift surveys 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 that scales with the catastrophic rate $f_c$. While this effect is negligible for DESI galaxy populations ($f_c=1\%$), the slitless-like errors, combining redshift uncertainty with $f_c=5\%$ catastrophics, introduce significant biases in cosmological constraints. In this case, we observe $6\%$ to $16\%$ shifts ($\sim2.2σ$ level) in estimating the fractional growth rate $df\equiv f/f^{\rm{fid}}$ and the log primordial amplitude $\ln(10^{10} A_{s})$. Applying the correction factor $(1-f_c)^2$ on the galaxy power spectrum mitigates the bias but weakens the parameter constraints due to new degeneracies. Alternatively, fixing $f_c$ to its expected value restores the constraining power with a modest bias of $1.0σ$. Our results indicate that for space-based slitless surveys such as \textit{Euclid}, at minimum accurate estimation of $f_c$ and its incorporation into the clustering model are essential 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 $w_0$ and $w_a$, but can degrade constraints on the summed neutrino mass $\sum m_ν$ by up to 80% in the worst case.

Figures (10)

• Figure 1: Comparisons of redshift error ($\Delta v_{\rm{error}}$) distributions. Left: Typical LRG-like and QSO-like redshift uncertainties, modeled by Gaussian smearing with $\sigma_{\Delta v}$ or Lorentzian smearing with $\mathrm{w}_{\Delta v}$. Right: ELG-like catastrophics with $f_c=1\%$ and hypothetical slitless-like errors with LRG-like redshift uncertainty (left part) and $f_c=5\%$ catastrophics (right part). These distributions are used to generate the velocity dispersion caused by redshift errors.
• Figure 2: Power spectrum monopole and quadrupole ratios from the mean of 500 mocks (dashed line) compare to theoretical model (solid lines). The shaded regions correspond to the errors from the standard deviation of the 500 mocks divided by 5. Left: Comparison between the ratios from mocks contaminated by Gaussian or Lorentzian smearing (characterized by $\sigma_{\Delta v}$ and $\mathrm{w}_{\Delta v}$ respectively) relative to clean mocks with the Gaussian Damping (GD) or Lorentzian Damping (LD) factor. Right: Comparison between $f_c=1\%$ and $5\%$ contamination mock ratios with the $(1-f_c)^2$ scaling.
• Figure 3: Comparison of power spectrum monopole (left) and quadrupole (right) between clean mocks and mocks contaminated by redshift uncertainties. The error bars, $\sigma$, are rescaled to match an effective survey volume of $V_{25}$. The lower panels show their residuals in units of clean mocks $\sigma$, with the dotted line indicating the $3\sigma$ threshold. In QSO-like Gaussian or Lorentzian smearing cases, we see significant deviations ($>3\sigma$) for $k \gtrsim 0.09 \, h \, \rm{Mpc}^{-1}$.
• Figure 4: Similar to \ref{['fig:plot_clustering_pk_ru']} comparing clean mocks and mocks contaminated by ELG-like catastrophics and slitless-like errors. Redshift catastrophics introduce an overall suppression on power spectrum amplitude, leading $>3\sigma$ difference for sliltess-like errors.
• Figure 5: Distributions of the best-fit values for ShapeFit compressed parameters. Scatter plots compare results from clean and contaminated mocks in \ref{['tab:mock catalogs']}. Each point represents one fit to the mean of 25 random mocks, with the covariance rescaled to volume $V_{25}$. The corresponding marginalized histograms are shown in the right and top subpanels. The parameter estimates remain consistent across most cases, except for $df$, which shows a notable deviation in mocks contaminated by slitless-like errors.