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Fiducial-Cosmology-dependent systematics for the DESI 2024 Full-Shape Analysis

This paper demonstrates that systematic biases in DESI 2024 DR1 full-shape cosmological inference arising from mismatches between the fiducial and true cosmologies are negligible, remaining well below statistical uncertainties for both full-modelling and ShapeFit analysis methods across various cosmological scenarios.

Original authors: R. Gsponer, S. Ramirez-Solano, F. Rodríguez-Martínez, M. Vargas-Magaña, S. Novell-Masot, N. Findlay, H. Gil-Marín, P. Zarrouk, S. Nadathur, A. Rocher, S. Brieden, A. Pérez-Fernández, J. Aguilar, S. Ah

Published 2026-06-10

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CC BY 4.0

Original authors: R. Gsponer, S. Ramirez-Solano, F. Rodríguez-Martínez, M. Vargas-Magaña, S. Novell-Masot, N. Findlay, H. Gil-Marín, P. Zarrouk, S. Nadathur, A. Rocher, S. Brieden, A. Pérez-Fernández, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, F. J. Castander, T. Claybaugh, A. Cuceu, A. de la Macorra, A. de Mattia, Arjun Dey, P. Doel, A. Font-Ribera, J. E. Forero-Romero, E. Gaztañaga, S. Gontcho A Gontcho, G. Gutierrez, J. Guy, C. Hahn, H. K. Herrera-Alcantar, K. Honscheid, C. Howlett, D. Huterer, M. Ishak, R. Joyce, R. Kehoe, D. Kirkby, T. Kisner, A. Kremin, O. Lahav, C. Lamman, M. Landriau, L. Le Guillou, M. E. Levi, C. Magneville, M. Manera, A. Meisner, R. Miquel, J. Moustakas, E. Mueller, N. Palanque-Delabrouille, W. J. Percival, F. Prada, I. Pérez-Ràfols, G. Rossi, L. Samushia, E. Sanchez, D. Schlegel, M. Schubnell, H. Seo, J. Silber, D. Sprayberry, G. Tarlé, B. A. Weaver, C. Zhao, R. Zhou, H. Zou

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 you are trying to map the entire universe, measuring the distances between millions of galaxies to understand how the cosmos is expanding. To do this, you need a "ruler" and a "map." But here's the catch: you don't know the exact size of the ruler or the true shape of the map yet. So, you have to make an educated guess about them. This guess is called the fiducial cosmology.

This paper is essentially a "stress test" for the Dark Energy Spectroscopic Instrument (DESI), a massive telescope project. The researchers wanted to answer a simple question: Does it matter if our initial guess about the universe's shape is slightly wrong?

Here is the breakdown of their investigation using everyday analogies:

1. The Setup: The "Perfect" Simulation

The researchers didn't just look at real data immediately. First, they built a perfect digital twin of the universe using supercomputers (called AbacusSummit). In this digital twin, they knew the "true" answer exactly—it was based on the best current scientific model (Planck 2018).

They then created a set of "fake" data from this perfect universe. This is like having a test answer key before taking a math exam.

2. The Test: Changing the "Ruler"

Next, they ran their analysis software on this fake data five different times. Each time, they told the software to assume a different universe as its starting point (its "fiducial cosmology").

Think of it like trying to measure a room with a tape measure that is slightly too long or too short.

Scenario A: They used the "correct" ruler (the baseline model).
Scenario B: They used a ruler that assumed the universe had less matter.
Scenario C: They used a ruler that assumed dark energy was changing over time.
Scenario D & E: They used rulers based on other popular theories or even the specific results DESI found in its first year of real data.

3. The Two Methods: "Full-Shape" vs. "Compressed"

The paper tests two different ways of reading the data, which they call Full-Modelling (FM) and ShapeFit (SF).

Full-Modelling (FM): Imagine trying to solve a complex puzzle by looking at every single piece, its color, its shape, and how it fits with its neighbors. This method tries to figure out the fundamental properties of the universe (like how much dark matter there is) directly from the raw data.
ShapeFit (SF): Imagine looking at the puzzle and just measuring the overall "stretch" or "slope" of the picture without worrying about every tiny detail. This method compresses the data into a few key numbers (like a "stretch factor") to see how the universe is expanding.

4. The Results: "It's All Good"

The researchers compared the results from their "wrong" rulers against the "perfect" answer key. They asked: Did using a slightly wrong starting guess cause the final answer to be wildly incorrect?

The findings were very reassuring:

For the "Full-Modelling" method: Even when they used a ruler based on a very different universe (like one with changing dark energy), the final answer was only off by a tiny, tiny amount. The error was less than 0.22% of the statistical uncertainty of the real DESI data. It's like measuring a football field and being off by less than the width of a human hair.
For the "ShapeFit" method: The results were similarly robust. The biggest shift they saw was in a specific parameter related to the "slope" of the universe, but even that was less than 0.45% of the expected error margin.

5. The "Why" and the "So What"

The paper explains that when you assume the wrong starting point, it can distort the data (like looking at a reflection in a funhouse mirror). However, the DESI analysis methods are so flexible and powerful that they can "undo" these distortions.

The Analogy: If you look at a straight stick through a curved piece of glass, it looks bent. But if you know how the glass curves, you can mathematically straighten the image back out. The researchers found that even if they guessed the wrong shape of the glass, their math was good enough to still figure out that the stick was actually straight.

Conclusion

The paper concludes that for the current level of precision DESI has achieved (Data Release 1), it does not matter if our initial guess about the universe is slightly off. The systematic errors introduced by choosing the wrong "fiducial cosmology" are so small that they are completely drowned out by the natural statistical noise of the data.

In short: The DESI team can rest easy. Their "map" and "ruler" are robust enough that even if their starting assumptions aren't perfect, their final map of the universe will still be accurate. They don't need to add extra "error bars" to their results just to account for guessing the wrong starting model.

Technical Summary: Fiducial-Cosmology-dependent systematics for the DESI 2024 Full-Shape Analysis

Problem Statement
The Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) full-shape analysis aims to constrain cosmological parameters by modeling the galaxy power spectrum across a broad range of scales. A critical component of this analysis is the choice of a "fiducial cosmology," which serves two distinct roles:

Grid Cosmology: Used to convert observed redshifts and angular positions into comoving coordinates. An incorrect assumption here introduces anisotropic distortions (Alcock-Paczynski effect) and shifts the Baryon Acoustic Oscillation (BAO) peak.
Template Cosmology: In compressed analyses, a fixed fiducial model generates the power spectrum template. Discrepancies between this template and the true cosmology can bias inferred parameters.

This study assesses the systematic shifts introduced when the assumed fiducial cosmology deviates from the true underlying cosmology of the data. The goal is to quantify whether these shifts are negligible compared to the statistical uncertainties of DESI DR1, thereby validating the robustness of the analysis pipeline.

Methodology
The authors utilize a suite of 25 "complete" AbacusSummit-2 DR1 mock catalogues. These mocks are generated based on the Planck 2018 best-fit $\Lambda$ CDM cosmology (the "baseline" or true cosmology). The analysis systematically varies the fiducial cosmology assumed during the pipeline processing to five secondary models:

Low- $\Omega_m$ : Lower matter density.
Thawing-DE: A dynamical dark energy model ( $w_0wa$ CDM).
High- $N_{\text{eff}}$ : Higher effective number of neutrino species.
Low- $\sigma_8$ : Reduced clustering amplitude (applied only to the template in ShapeFit).
DESI BAO: The best-fit $w_0wa$ CDM cosmology derived from DESI DR1 BAO measurements.

The study employs two complementary full-shape analysis approaches:

Full-Modelling (FM): Directly infers cosmological parameters ( $\theta_{\text{cosmo}}$ ) within a specific model (either $\Lambda$ CDM or extended $w_0wa$ CDM) using the Effective Field Theory of Large Scale Structure (EFTofLSS).
ShapeFit (SF): Compresses the power spectrum information into model-independent parameters ( $\alpha_\parallel, \alpha_\perp, f\sigma_{s8}, m, n$ ) before interpreting them in terms of a cosmological model.

For the extended $w_0wa$ CDM models, which suffer from projection effects when analyzed with DESI data alone, the authors incorporate a mock Type Ia Supernova (SNe Ia) dataset (Pantheon+ like) to break degeneracies and provide robust constraints. Systematic shifts are quantified as the difference in Maximum A Posteriori (MAP) values between the secondary fiducial runs and the baseline run, normalized by the statistical uncertainty of the 25 mocks ( $\sigma_{V25}$ ) and the realistic DESI DR1 uncertainty ( $\sigma_{\text{DR1}}$ ).

Key Contributions

Quantification of Systematics: The paper provides the first comprehensive quantification of fiducial cosmology-dependent systematics for the DESI full-shape analysis across multiple tracers (BGS, LRG, ELG, QSO) and redshift bins.
Dual Approach Validation: It validates both the Full-Modelling and ShapeFit pipelines against fiducial mismatches, demonstrating that the results are consistent across different analysis philosophies.
Template vs. Grid Decomposition: The study isolates the specific contributions of grid cosmology mismatches versus template cosmology mismatches, revealing that template mismatches primarily affect early-time physics parameters (shape parameters), while grid mismatches affect late-time geometric parameters.
Beyond $\Lambda$ CDM Stress Testing: The analysis explicitly tests the robustness of the pipeline when the true cosmology is non- $\Lambda$ CDM (thawing DE, DESI BAO best-fit), showing that restricted $\Lambda$ CDM models fail to capture these distortions, while extended models recover unbiased results when combined with external data.

Results

Full-Modelling (FM):
- For $\Lambda$ CDM-like secondary cosmologies (Low- $\Omega_m$ , High- $N_{\text{eff}}$ ), systematic shifts are well below statistical noise, with maximum deviations of 0.22 $\sigma_{\text{DR1}}$ in the combined tracer analysis.
- When interpreting extended grid cosmologies (Thawing-DE, DESI BAO) using a restricted $\Lambda$ CDM model, significant biases appear (up to 6.4 $\sigma_{V25}$ ), confirming the necessity of using the correct model class.
- When analyzing extended grid cosmologies with a consistent $w_0wa$ CDM model (including SNe Ia), shifts drop to negligible levels, with a maximum of 0.12 $\sigma_{\text{DR1+SN}}$ .
ShapeFit (SF):
- Shifts in compressed parameters remain below 0.45 $\sigma_{\text{DR1}}$ for all tracers and cosmologies.
- The largest shifts occur in the reparameterized shape parameter $(m+n)$ , particularly for Low- $\Omega_m$ and High- $N_{\text{eff}}$ cases, reaching 1.73 $\sigma_{V25}$ (still below the 2 $\sigma$ significance threshold).
- Decomposition analysis shows that for Low- $\Omega_m$ and High- $N_{\text{eff}}$ , the bias is dominated by the template cosmology mismatch, whereas for Thawing-DE and DESI BAO, it is dominated by the grid cosmology mismatch.

Significance and Claims
The paper concludes that the choice of fiducial cosmology introduces negligible systematic errors for the DESI DR1 full-shape analysis.

The systematic shifts are subdominant to the statistical uncertainties of the current dataset.
Consequently, no additional systematic error budget contribution is required from this source for the DESI DR1 results.
The analysis demonstrates that the full-shape pipeline is robust against moderate variations in the fiducial model.
The authors note that while the current impact is minor, future data releases with higher statistical precision will require a re-evaluation of these systematics, particularly if evidence for evolving dark energy persists, necessitating an expansion of the tested fiducial cosmologies.