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The Impact of Spectroscopic Redshift Errors on Cosmological Measurements

This study demonstrates that while standard spectroscopic redshift errors have minimal impact on cosmological parameters for surveys like DESI, the specific combination of redshift uncertainty and higher catastrophic failure rates typical of space-based slitless surveys (e.g., Euclid) can significantly bias growth rate and primordial amplitude measurements and severely degrade constraints on neutrino mass, necessitating accurate estimation and modeling of these errors to ensure unbiased cosmological inference.

Original authors: Shengyu He, Jiaxi Yu, Antoine Rocher, Daniel Forero-Sánchez, Jean-Paul Kneib, Cheng Zhao, Etienne Burtin, Jiamin Hou

Published 2026-06-18

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CC BY 4.0

Original authors: Shengyu He, Jiaxi Yu, Antoine Rocher, Daniel Forero-Sánchez, Jean-Paul Kneib, Cheng Zhao, Etienne Burtin, Jiamin Hou

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, three-dimensional city filled with billions of stars and galaxies. Astronomers want to map this city to understand how it was built and how it's growing. To do this, they use a special tool called a spectrograph, which acts like a high-tech barcode scanner. It reads the light from galaxies to determine their "redshift"—a measure of how fast they are moving away from us, which tells us their distance.

However, just like any scanner, this tool isn't perfect. Sometimes it makes small, fuzzy mistakes, and sometimes it gets completely confused. This paper investigates how these "scanner errors" mess up our map of the universe and whether we can fix them.

Here is a breakdown of the paper's findings using simple analogies:

1. The Two Types of Scanner Glitches

The authors identify two main ways the redshift scanner can go wrong:

Redshift Uncertainty (The "Fuzzy Lens"): Imagine looking at a distant streetlight through a slightly foggy window. The light is still there, but it looks a tiny bit blurry or shifted. This happens to every galaxy in the survey. It's a small, random error caused by the limits of the instrument or the natural movement of the gas inside the galaxy.
- The Effect: This blurriness acts like a "dampener." It smooths out the sharp details of the cosmic map, making the clustering of galaxies look slightly less distinct, especially on small scales.
Catastrophic Failures (The "Wrong Zip Code"): Imagine a scanner that accidentally reads a street sign for "Main Street" and assigns it to "Main Street, Australia" instead of "Main Street, Ohio." This happens to a small fraction of galaxies (maybe 1% to 5%). The scanner misidentifies the galaxy's spectral lines entirely, sending it to the wrong distance.
- The Effect: This is much worse than the fuzziness. It doesn't just blur the map; it effectively removes those galaxies from the correct location, causing the overall "loudness" (amplitude) of the cosmic signal to drop significantly.

2. The Two Survey Styles: Fiber vs. Slitless

The paper compares two types of surveys:

DESI (Ground-based): Uses "fibers" (like tiny straws) to pick up light from one galaxy at a time. It's very precise, like a laser pointer.
Euclid (Space-based): Uses "slitless" spectroscopy. It looks at the whole sky at once without straws, like a wide-angle camera. This is faster and catches more galaxies, but it's more prone to errors because the light from different galaxies can overlap, making it harder to tell them apart.

3. What Happens When We Analyze the Data?

The researchers created 500 fake universes (mocks) to test how these errors affect their calculations. They found:

The "Fuzzy Lens" is Manageable: The small blurriness (uncertainty) changes the data, but the mathematical models astronomers use are flexible enough to absorb this change. It's like a sponge soaking up a little water; the model adjusts its internal "sponge" settings (called counterterms) to hide the error. The final results for the universe's properties remain accurate (within 5%).
The "Wrong Zip Code" is Dangerous for Space Missions:
- For ground-based surveys (DESI), the error rate is low (about 1%). The impact is tiny and barely noticeable.
- For space-based surveys (Euclid), the error rate could be higher (around 5%). This causes a massive drop in the signal strength. If astronomers ignore this, they will underestimate key numbers, like how fast the universe is growing or how much "primordial energy" existed at the Big Bang. They found these errors could shift results by 6% to 16%, which is a huge mistake in cosmology (about 2.2 standard deviations off).

4. How to Fix the "Wrong Zip Code" Problem

The paper proposes two ways to fix the catastrophic errors in space surveys:

The "Volume Discount" Method: They found that if you simply multiply the data by a correction factor of $(1 - \text{error rate})^2$ $(1 - error rate)^{2}$ , you can fix the bias.
- The Catch: If you treat the error rate as a "free variable" (letting the computer guess it), you fix the bias, but you lose precision. It's like trying to solve a puzzle where you don't know how many pieces are missing; you get the right picture, but you aren't sure how confident you are in it.
- The Better Fix: If you fix the error rate to a known, expected value (e.g., "We know 5% of our data is bad"), you get the correct answer and keep your high precision.

5. What About Dark Energy and Neutrinos?

The researchers also checked if these errors mess up more complex theories:

Dark Energy: The errors didn't change the estimated behavior of dark energy (the force pushing the universe apart). However, they might make the statistical "fog" slightly thicker, making it harder to distinguish between different theories.
Neutrino Mass: This is where it gets tricky. Neutrinos are tiny particles that also "smear" the cosmic map. Redshift errors do the exact same thing. When both happen at once, it's like trying to hear a whisper in a room with two people whispering at once. The model gets confused, and the ability to measure the total mass of neutrinos can degrade by up to 80%.

The Bottom Line

For ground-based surveys like DESI, these redshift errors are a minor annoyance that the current models handle well. However, for future space missions like Euclid, which use "slitless" technology, these errors are a major threat.

To get an unbiased map of the universe, space surveys must accurately estimate their error rate and build that number directly into their mathematical models. If they don't, they risk drawing the wrong conclusions about the fundamental nature of our universe.

Technical Summary: The Impact of Spectroscopic Redshift Errors on Cosmological Measurements

Problem Statement
Galaxy redshift surveys, such as the Dark Energy Spectroscopic Instrument (DESI) and the Euclid space mission, aim to constrain cosmological parameters (e.g., dark energy equation of state, neutrino mass, structure growth) with sub-percent precision using large-scale structure (LSS) clustering. However, spectroscopic redshift measurements are subject to systematic errors that persist even after standard calibration and quality cuts. These errors are categorized into two types:

Redshift Uncertainty: Small, statistical fluctuations in redshift measurements ( $\Delta z \sim 10^{-4}$ ) caused by instrumental noise and intrinsic spectral line widths.
Redshift Catastrophic Failures: Large deviations ( $\Delta z \sim 10^{-2}$ ) resulting from the misidentification of spectral lines or sky residuals, affecting a small fraction of the sample.

While previous studies have examined these errors individually, this work addresses the gap in understanding their combined impact on full-shape power spectrum analyses, particularly for space-based slitless surveys (like Euclid) which are more susceptible to both error types due to lower spectral resolution and source overlap.

Methodology
The authors utilize the Quijote N-body simulation suite to generate 500 mock galaxy catalogs based on a flat $\Lambda$ CDM fiducial cosmology (Planck 2018). To simulate observational systematics, they introduce specific redshift error profiles into the line-of-sight peculiar velocities of the halos:

Redshift Uncertainty: Modeled using Gaussian profiles (for LRG-like and QSO-like smearing) and a Lorentzian profile (to capture extended tails in QSO uncertainties).
Catastrophic Failures: Modeled using a log-normal distribution based on DESI DR1 ELG repeat observations.
Slitless-like Scenario: A hypothetical combined error model representing Euclid-like conditions, featuring LRG-like uncertainty ( $\sigma_{\Delta v} \approx 85.7$ km/s) and a higher catastrophic rate ( $f_c = 5\%$ ).

Cosmological inference is performed using two fitting strategies on the power spectrum monopole and quadrupole ( $0.02 \le k \le 0.2 \, h \text{ Mpc}^{-1}$ ):

ShapeFit: Compresses the data into physical parameters ( $\alpha_{iso}, \alpha_{ap}, f\sigma_8$ , shape parameters).
Full-Modeling: Directly fits cosmological parameters ( $h, \omega_{cdm}, \omega_b, \ln(10^{10}A_s), n_s$ ) using the Effective Field Theory (EFT) of LSS framework (via the FOLPS $\nu$ code).

The analysis compares "clean" mocks against contaminated mocks to quantify biases in parameter estimation.

Key Contributions and Results

Impact of Redshift Uncertainty:
- Redshift uncertainty introduces a scale-dependent damping effect on the power spectrum, suppressing amplitude more strongly at smaller scales (higher $k$ ).
- Result: This damping is effectively absorbed by the EFT counterterms (specifically $\alpha_2$ and $\alpha_4$ ). Consequently, cosmological parameter biases remain below 5% even when the damping is not explicitly modeled in the likelihood, provided the EFT framework is used.
Impact of Catastrophic Failures:
- Catastrophic failures suppress the overall power spectrum amplitude by a factor approximately scaling as $(1 - f_c)^2$ .
- DESI-like ( $f_c = 1\%$ ): The effect is negligible, introducing biases $< 6\%$ .
- Slitless-like ( $f_c = 5\%$ ): This scenario introduces significant biases. The fractional growth rate ( $d_f \equiv f/f_{fid}$ ) and the log primordial amplitude ( $\ln(10^{10}A_s)$ ) are underestimated by 6% to 16%, corresponding to a $\sim 2.2\sigma$ deviation from the true values.
Mitigation Strategies for Slitless Surveys:
- Applying a correction factor of $(1 - f_c)^2$ to the power spectrum model mitigates the bias.
- Freeing $f_c$ : Treating the catastrophic rate as a free parameter in the fit recovers unbiased values for $\ln(10^{10}A_s)$ (bias $< 0.1\sigma$ ) but degrades the constraint precision by 67% due to strong degeneracy between $f_c$ and the amplitude.
- Fixing $f_c$ : Fixing $f_c$ to its expected value restores the constraining power, leaving only a modest bias of 1.0 $\sigma$ .
Beyond $\Lambda$ CDM:
- Evolving Dark Energy ( $w_0, w_a$ ): Redshift errors do not introduce significant bias in the estimation of dark energy parameters. However, they may enhance projection effects (discrepancies between the mean posterior and the Maximum A Posteriori value), particularly for QSO-like smearing.
- Massive Neutrinos ( $\sum m_\nu$ ): Redshift uncertainty creates a degeneracy with neutrino mass because both suppress small-scale power (neutrinos via free-streaming, redshift errors via line-of-sight smearing). In the worst-case scenario (QSO-like Gaussian smearing), the upper limit on the sum of neutrino masses degrades by up to 80%. Catastrophic failures show negligible impact on neutrino mass constraints.

Significance and Claims
The paper claims that for space-based slitless surveys like Euclid, accurate estimation of the catastrophic failure rate ( $f_c$ ) and its incorporation into the clustering model are necessary to obtain unbiased cosmological inferences. While redshift uncertainty is manageable within standard EFT frameworks, the higher catastrophic rates expected in slitless surveys pose a non-negligible risk to amplitude-dependent parameters. The authors conclude that either fixing $f_c$ to a well-calibrated value or modeling it with a narrow prior is required to maintain statistical power while minimizing bias. The work provides a practical framework for interpreting and mitigating these systematics in upcoming full-shape analyses.