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Accurate modeling for 3 $\times$ 2pt analyses in Roman and Rubin: a study of model approximations

This paper systematically demonstrates that neglecting the Limber approximation, redshift-space distortions, or using inaccurate nonlinear matter power spectrum models in 3 $\times$ 2pt analyses for the Roman and Rubin surveys can induce significant cosmological biases exceeding $1\sigma$ to $2\sigma$ , thereby validating the necessity of precise modeling for these Stage-IV experiments.

Original authors: Junzhou Zhang, Chihway Chang, Jiachuan Xu, Vivian Miranda, Chun-Hao To, Haley Bowden, Kaili Cao, Tim Eifler, Roman HLIS Cosmology PIT

Published 2026-06-24

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CC BY 4.0

Original authors: Junzhou Zhang, Chihway Chang, Jiachuan Xu, Vivian Miranda, Chun-Hao To, Haley Bowden, Kaili Cao, Tim Eifler, Roman HLIS Cosmology PIT

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 measure the shape of a giant, invisible balloon floating in space. This balloon represents the universe, and its shape tells us about the invisible ingredients inside it, like dark matter and dark energy. To do this, astronomers use two main tools: they count how many galaxies are in different areas (like counting stars in a constellation) and they measure how the light from those galaxies gets stretched as it travels through space (like looking at a straw in a glass of water).

This paper is about making sure the "rulers" and "magnifying glasses" we use to measure this cosmic balloon are accurate enough for the next generation of super-powerful telescopes: the Roman Space Telescope and the Vera C. Rubin Observatory.

Here is the breakdown of what the authors did, using simple analogies:

The Problem: Three "Shortcuts" That Might Be Too Short

In the past, when astronomers analyzed data from older, less powerful telescopes, they used three common "shortcuts" (approximations) to make the math easier. It was like using a rough sketch instead of a high-definition photo because the sketch was "good enough" for the job.

However, the new telescopes (Roman and Rubin) are so powerful that they can see details the old ones couldn't. The authors asked: "Are these old shortcuts still good enough, or will they make our measurements of the universe wrong?"

They tested three specific shortcuts:

The "Flat Map" Shortcut (Limber Approximation):
- The Analogy: Imagine trying to calculate the distance between two cities on a globe. The "shortcut" is pretending the Earth is a flat piece of paper. For short distances, this works fine. But for very long distances or very specific angles, the flat map gives you the wrong answer.
- The Finding: For the new, super-precise telescopes, pretending the universe is "flat" in the math causes significant errors. It's like trying to navigate the ocean using a flat map of a small pond; you'll end up in the wrong place.
The "Still Water" Shortcut (Ignoring Redshift-Space Distortions):
- The Analogy: Imagine you are watching fish swim in a river. If you only look at where they are, you get one picture. But if the river is flowing fast, the fish appear to be in a different spot than they actually are because the water is pushing them. The "shortcut" was ignoring the river's current and assuming the fish were just floating in still water.
- The Finding: Galaxies aren't just sitting still; they are moving with the flow of the universe. Ignoring this "current" (Redshift-Space Distortions) makes the map of the universe look distorted, leading to wrong conclusions about how much dark matter is there.
The "Old Recipe" Shortcut (Nonlinear Matter Power Spectrum):
- The Analogy: Imagine you are baking a cake. You have an old, simple recipe (HMCode) that works okay for a basic cake. But now you have a new, high-tech oven (the new telescopes) that can bake a cake so perfectly that the tiny differences in ingredients matter. The authors compared the old recipe to a new, ultra-precise recipe (EuclidEmulator2) based on super-computer simulations.
- The Finding: The old recipe is close, but for the new ovens, it introduces small but noticeable errors in the final taste (the cosmological results).

The Experiment: A Simulation Race

The authors didn't wait for the telescopes to launch. Instead, they built a virtual universe inside a computer. They ran the same "race" twice:

The "Perfect" Race: Using the most accurate, complex math possible (no shortcuts).
The "Shortcut" Race: Using the three shortcuts mentioned above.

They then compared the results to see how far off the "Shortcut" racers were from the "Perfect" racers.

The Results: The Shortcuts Are Dangerous

The study found that for the new, powerful telescopes, all three shortcuts are dangerous.

The Magnitude of Error: If you use these shortcuts, your measurement of the universe's shape could be off by 1 to 3 "sigma" (a statistical way of saying "very wrong"). In the world of science, being off by 1 sigma is a warning sign; being off by 2 or 3 sigma means you are likely drawing the wrong conclusion entirely.
The Impact:
- For the Roman telescope, the errors were significant enough to be concerning (around 1 sigma).
- For the Rubin telescope, which is even more powerful, the errors were even worse (up to 3 sigma).
- If you combine all three shortcuts, the error becomes massive, potentially leading scientists to believe the universe is made of different ingredients than it actually is.

The Conclusion: Throw Away the Old Maps

The paper concludes that for the next generation of cosmology, we cannot rely on the "rough sketches" and "old recipes" of the past.

We need better math: We must use the complex, "non-flat" calculations (Non-Limber) even though they are harder to compute.
We need to account for the flow: We must include the effects of galaxies moving with the cosmic current (RSD).
We need better recipes: We must use the most precise models for how matter clumps together (EuclidEmulator2).

In short: The universe is too complex, and our new telescopes are too powerful to get away with "good enough" math. If we want to understand the universe correctly, we have to do the hard work of using the most accurate models possible.

Technical Summary: Accurate Modeling for 3×2pt Analyses in Roman and Rubin

Problem Statement
Modern cosmology relies heavily on "3×2pt" analyses, which combine galaxy clustering, galaxy-galaxy lensing, and cosmic shear to constrain cosmological parameters. While this framework has been successfully applied to Stage-III surveys (e.g., DES, KiDS), the upcoming Stage-IV surveys—specifically the Nancy Grace Roman Space Telescope's High Latitude Imaging Survey (HLIS) and the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST)—will provide unprecedented statistical power. The authors posit that modeling approximations acceptable for Stage-III data may introduce significant biases in Stage-IV constraints. This paper systematically investigates three specific modeling approximations commonly used in 3×2pt analyses:

The application of the Limber approximation for projecting 3D power spectra to angular scales.
The neglect of Redshift-Space Distortions (RSD) in the galaxy overdensity field.
The use of less accurate models for the nonlinear matter power spectrum (specifically comparing HMCode against EuclidEmulator2).

Methodology
The study utilizes a simulated likelihood analysis framework implemented in CoCoA (CosmoLike-Cobaya Architecture), a pipeline developed by the Roman HLIS Cosmology PIT. To ensure robustness, the authors first validated CoCoA against the established Core Cosmology Library (CCL), which serves as the standard for the Rubin LSST Dark Energy Science Collaboration (DESC).

Survey Configurations: The analysis forecasts constraints for a 5-year Roman HLIS dataset (medium tier) and a 10-year Rubin LSST dataset. Both utilize 10 lens-galaxy bins and varying numbers of source-galaxy bins (8 for Roman, 5 for Rubin).
Modeling Framework: The analysis assumes a flat $\Lambda$ CDM cosmology with five free parameters ( $A_s, n_s, H_0, \Omega_b, \Omega_m$ ). Nuisance parameters include photo-z shifts, shear calibration biases, intrinsic alignment (NLA model), and linear galaxy bias.
Scale Cuts: To mitigate uncertainties from baryonic feedback and nonlinear galaxy bias, the authors apply conservative scale cuts. In real space, this corresponds to a minimum transverse radius of 6 Mpc/h for lensing and 8 Mpc/h for clustering. In harmonic space, these translate to specific multipole ranges ( $20 < \ell < 4000$ ).
Experimental Design: The authors define five model scenarios to isolate the effects of the approximations:
1. Baseline: Non-Limber for clustering, RSD included, EuclidEmulator2 for nonlinear power spectrum.
2. Limber: Uses Limber approximation for clustering.
3. noRSD: Omits RSD corrections.
4. HMCode: Uses HMCode instead of EuclidEmulator2.
5. Combined: Uses Limber, omits RSD, and uses HMCode.

Key Results
The study quantifies the impact of these approximations on both the data vectors (via $\Delta\chi^2$ ) and the resulting cosmological constraints (bias in the $\Omega_m - S_8$ plane).

Code Validation: The comparison between CoCoA and CCL showed excellent agreement, with $\Delta\chi^2$ values well below 1 for the fiducial settings, confirming the reliability of the modeling pipeline.
Individual Approximation Impacts:
- Limber Approximation: Neglecting the non-Limber calculation for galaxy clustering induces biases of ~0.7–0.8 $\sigma$ for Roman and ~1.8–2.0 $\sigma$ for Rubin. The effect is more pronounced in harmonic space than real space because scale cuts remove less of the affected large-scale modes in harmonic space.
- Redshift-Space Distortions (RSD): Neglecting RSD produces biases comparable to or slightly larger than the Limber approximation, reaching ~0.7–0.8 $\sigma$ for Roman and ~2.0–2.3 $\sigma$ for Rubin. The authors note that RSD is the dominant effect between the two, as the Limber approximation inherently suppresses RSD contributions.
- Nonlinear Power Spectrum: Switching from EuclidEmulator2 to HMCode results in smaller biases (~0.6 $\sigma$ for Roman, ~1.0–1.2 $\sigma$ for Rubin). This is because the differences between these models are primarily on small scales, which are largely removed by the fiducial scale cuts.
Combined Effects: When all three approximations are applied simultaneously, the biases accumulate. For Rubin, the combined bias reaches ~2.8 $\sigma$ (real space) and ~3.1 $\sigma$ (harmonic space). For Roman, the combined bias is ~1.0–1.1 $\sigma$ .
Survey Sensitivity: The biases are consistently larger for Rubin than for Roman due to Rubin's greater constraining power. The authors note that while they assumed a "medium tier" for Roman, a "wide tier" configuration would likely yield even tighter constraints and potentially larger biases if approximations are used.

Significance and Conclusions
The paper concludes that for Stage-IV surveys, the standard approximations used in Stage-III analyses are insufficient. Neglecting any of the three investigated effects can induce cosmological biases approaching or exceeding 1 $\sigma$ for Roman and 2 $\sigma$ for Rubin.

The authors emphasize three main implications for future Stage-IV analyses:

Non-Limber Algorithms: It is critical to optimize non-Limber algorithms to ensure they are numerically stable and computationally efficient, as the Limber approximation is no longer sufficient for galaxy clustering in high-precision surveys.
RSD Modeling: The linear-order RSD effect has a large impact on data vectors and constraints, motivating the development and inclusion of more realistic RSD models.
Nonlinear Power Spectrum: The choice of the nonlinear matter power spectrum model is significant, particularly when combined with specific scale cut strategies.

The study serves as a validation of the CoCoA pipeline against CCL and provides a quantitative basis for requiring higher-fidelity modeling in the final data releases of the Roman and Rubin surveys. The authors suggest future work should extend these findings to include nonlinear galaxy bias, more complex intrinsic alignment models, and baryonic feedback, as well as investigate the combination of Roman's medium and wide tiers.

The Problem: Three "Shortcuts" That Might Be Too Short

The Experiment: A Simulation Race

The Results: The Shortcuts Are Dangerous

The Conclusion: Throw Away the Old Maps

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