Euclid preparation CIX. Baryon acoustic oscillation analysis of photometric galaxy clustering in configuration space

arXiv:2503.11621 · astro-ph.CO · Submitted 2025-03-14 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Today's paper: "Euclid preparation CIX. Baryon acoustic oscillation analysis of photometric galaxy clustering in configuration space".

Jocelyn: This paper presents an analysis of Baryon Acoustic Oscillation (BAO) signals extracted from photometric galaxy clustering data using the Flagship mock catalogue from the Euclid mission.

Vera: First, who's behind it and why it matters.

Title and authors: Vera: So, we're looking at the paper titled "Euclid preparation CIX. Baryon acoustic oscillation analysis of photometric galaxy clustering in configuration space," and it seems like the focus is really on using those photometric galaxy clustering data to measure baryon acoustic oscillations. It's about taking what we see from the Euclid survey and trying to figure out how far away things are in the Universe by looking at these characteristic density patterns.

Jocelyn: I agree, Vera, it sounds like this paper is digging into how these large-scale structure signals evolve across different redshifts using photometric redshift information. It's not just one static measurement; it’s trying to map out the expansion history of the Universe by looking at how that BAO scale shifts over time.

Subrahmanyan: From a theoretical standpoint, this work tackles a complex challenge: extracting cosmological information from photometric data where you don't know the exact redshift of every galaxy, which is inherently messy. This paper tries to bridge that gap between noisy observational data and precise cosmological models.

Vera: Exactly, it’s about using those mock catalogues from Euclid to test our models of cosmic expansion. It’s a crucial step in preparing for the actual survey by seeing how well the signal we expect to see actually comes out when we use photometric redshifts.

Jocelyn: And what interests me is that they are using a tomographic approach across thirteen redshift bins, which means they're slicing the data up to see how things look at different epochs in cosmic time.

Subrahmanyan: That tomographic approach is key because it allows you to constrain the evolution of the Universe’s expansion history rather than just getting a single snapshot of parameters. It lets us see how dark energy or matter density might have changed over cosmic time.

Vera: Right, and they are using this method to constrain cosmological parameters like the reduced Hubble constant and other densities, which is exactly what we need to know about the fundamental makeup of our Universe.

Jocelyn: It sounds like a very practical application for those photometric galaxy clustering results that we've been discussing.

Subrahmanyan: Indeed, it moves the field from just measuring structure to constraining the dynamics driving that structure formation throughout cosmic history.

The paper's summary: Vera: So, summarizing what this paper is actually doing, they are applying a template-fitting method to the two-point angular correlation function, w(θ), which is a standard way to measure BAO scales. They use their Flagship mock catalogue to test if their model of how the signal looks matches reality.

Jocelyn: I think it’s important that they are not just measuring one number; they are extracting thirteen different alpha parameters, one for each redshift bin, which lets them track the evolution of the BAO scale as a function of time.

Subrahmanyan: That tracking capability is what makes this analysis powerful; we aren't just getting a single constraint on expansion at one moment, but we are mapping out how things evolve. This directly relates to understanding the physics behind dark energy or whatever is accelerating the expansion.

Vera: They then do a joint analysis across all those redshift bins using Markov Chain Monte Carlo and profile likelihood techniques to get one combined constraint on that transverse Alcock–Paczynski parameter, alpha, at an effective redshift of z eff = zero point seven seven.

Jocelyn: And they report some very specific results for this joint analysis: alpha(z eff = zero point seven seven) = one point zero zero one one pluszero point zero two three-zero point zero two three at the sixty-eight percent confidence level, and from that, they derive constraints on h being around forty-five percent, b at ninety-one percent, and cdm at seven point seven percent.

Subrahmanyan: Those derived values are interesting because they align reasonably well with the expectations of the Flagship simulation cosmology, which gives us a good benchmark for what we should see if our underlying cosmological model is correct.

Vera: It shows that this method is providing a significant improvement over what we currently have, offering a three-fold improvement over current constraints from the Dark Energy Survey (uncertainty of plus or minus zero point zero two three at z eff = zero point eight five with the same observable).

Jocelyn: That factor of three improvement is really significant for precision cosmology, and it shows that using this tomographic approach with photometric data can yield much tighter constraints than previous methods.

Subrahmanyan: It confirms that structure formation physics, modeled through the galaxy density field transfer function and linear Redshift Space Distortions contributions defined in equations (four) and (five), is robust enough to yield these precise results.

The paper's improvements: Vera: The authors really highlight how they tested the robustness of their findings against a bunch of different analysis choices, which is really important for building confidence in the results. They showed things like scale cuts as grey bands and explored different cut-offs, finding a clear cut-off at theta = one for the bias parameter alpha-one.

Jocelyn: And they also made sure to check how sensitive their results are to things like the choice of fitting templates—they tested polynomial orders—and how they handled nuisance parameters like redshift-space distortions, RSD. They found that the template nuisance parameters compensate for RSD effects, and the relative difference in alpha averaged across all redshift bins was only zero point two five percent.

Subrahmanyan: That level of compensation is quite reassuring; it means their core measurement isn't overly dependent on assumptions about how galaxy peculiar velocities distort the clustering signal. It suggests that the underlying BAO feature is well-isolated from those secondary effects.

Vera: They also tested excluding individual redshift bins to see what happens, and they found that bin eleven which has a high redshift of z eff = one point two four five, significantly decreases alpha by one sigma across all bins.

Jocelyn: So the paper emphasizes that while their main analysis is strong, they have to be careful about things like scale cuts and which redshift bins you choose when you're trying to build a final result.

Subrahmanyan: It’s an important methodological point for the community; knowing exactly where the limitations lie in terms of setup choices helps us design better future surveys.

Conclusion: Vera: To wrap things up, this paper on "Euclid preparation CIX. Baryon acoustic oscillation analysis of photometric galaxy clustering in configuration space" shows that we can indeed get strong constraints on cosmological parameters like h, b, and cdm using the Euclid mock data through a tomographic BAO approach.

Jocelyn: The main implication is that this method gives us a way to push the precision of our cosmology by achieving that three-fold improvement over previous constraints, which really helps narrow down the allowed parameter space for dark energy models.

Subrahmanyan: From a theoretical perspective, this work confirms that our understanding of structure formation physics is consistent with what we expect from the Flagship simulation when we look at these cosmological parameters.

Vera: It’s encouraging to see how well the results match our expectations, especially given the robustness they showed against various analysis choices, which gives us a solid footing for future work.

Jocelyn: I think it’s clear that this is a very useful technique for using photometric data from large surveys to probe the Universe's expansion history in detail.

Subrahmanyan: In essence, this paper lays a strong foundation for how we can use these clustering measurements to constrain cosmological parameters more tightly than ever before.

Euclid Collaboration

astro-ph.CO

Submitted: 2025-03-14

Updated: 2026-09-30

Comments: 20 pages, 18 figures, A&A, 713, A281 (2026)

Journal ref: A&A, 713, A281 (2026)

DOI: 10.1051/0004-6361/202554545

Code: https://github.com/fabienlacasa/PySSC

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 83/100

The gist: This paper presents an analysis of Baryon Acoustic Oscillation (BAO) signals extracted from photometric galaxy clustering data using the Flagship mock catalogue from the Euclid mission.

Key concepts

Baryon Acoustic Oscillation (BAO)
BAO refers to characteristic patterns in the distribution of galaxies caused by acoustic oscillations in the early universe. These patterns leave a standard 'ruler' imprinted on the galaxy clustering. Measuring this ruler allows scientists to map out the expansion history of the Universe and constrain cosmological parameters.
Galaxy Two-Point Angular Correlation Function, w($\theta$)
This function measures how galaxies are clustered in space based on their angular separation ($\theta$). It is a primary observable used in this study. By analyzing how this function changes with redshift, researchers can probe the growth of structure and constrain cosmological models.
Alcock–Paczynski Parameter ($\alpha$)
$\alpha$ is a parameter derived from comparing the measured BAO scale to a theoretical fiducial model. It quantifies any distortion in the apparent shape of the BAO peak caused by errors in measuring distances or assuming an incorrect cosmological model. Fitting $\alpha$ helps determine if the assumed cosmology matches reality.
Tomographic Approach
The tomographic approach involves dividing the observed data into multiple redshift bins. This allows researchers to study how galaxy clustering and BAO signals evolve at different epochs (redshifts). Using 13 bins provides a detailed look at the Universe's expansion history across various time periods.

Terminology

Summary

This paper presents an analysis of Baryon Acoustic Oscillation (BAO) signals extracted from photometric galaxy clustering data using the Flagship mock catalogue from the Euclid mission. By employing a tomographic approach across 13 redshift bins, the research aims to constrain cosmological parameters and infer the evolution of the Universe's expansion history. The findings demonstrate that this method provides a significant improvement over current constraints, offering a three-fold improvement over current constraints from the Dark Energy Survey (uncertainty of ± 0.023 at zeff = 0.85 with the same observable).

Observable and Theoretical Framework

The primary observable used in this analysis is the galaxy two-point angular correlation function, w(θ), defined as Equation (1). This function is related to the dimensionless power spectrum of primordial curvature perturbations, PΦ(k), which is modeled using HMCode implemented in CAMB. The theoretical model for w(θ) incorporates contributions from both the galaxy density field transfer function and the linear Redshift Space Distortions (RSD) contribution, defined in Equations (4) and (5). To accurately model large scales at small angular multipoles, non-Limber integrals are computed using the FKEM method, while the Limber approximation is used for larger multipoles.

BAO Signal Extraction and Template Fitting

The BAO scale is extracted by fitting a template to the measured w(θ). The template is defined as:

T (α, θ):= B wfid (αθ) + A0 + A1 θ − 1 + A2 θ − 2

The parameter of interest is the transverse Alcock–Paczynski parameter, α, which quantifies the shift of the BAO peak between the measured and fiducial correlation function. The analysis uses a template-fitting approach to extract this shift. The paper considers two analyses:

  1. Extracting the BAO scale in each of the 13 redshift bins, yielding 13 values of α to quantify its evolution as a function of time.

  2. Conducting a joint analysis of all redshift bins to constrain a single value of α at the effective redshift zeff = 0.77 using Markov Chain Monte-Carlo (MCMC) and profile likelihood techniques.

Cosmological Parameter Constraints

The extracted α parameters are directly proportional to the ratio DA/rs, drag, fid(1 + zeff), allowing constraints on the reduced Hubble constant h, the baryon density parameter omegab, and the cold dark matter density parameter omegacdm. The joint analysis yields:

α(zeff = 0.77) = 1.0011+0.0078 − 0.0079 at the 68% confidence level.

The resulting cosmological constraints are: h at 45%, omegab at 91%, and omegacdm at 7.7%. The analysis is robust against the choice of fiducial cosmology, as variations in h or ΛCDM parameters by up to 5% lead to a maximum expected variation of α of only around 1%.

Robustness and Analysis Choices

The study rigorously tests the robustness of the results against various analysis choices:

Scale cuts are shown as grey bands and are defined as θmin = 0.6°, θmax = θBAO + 2.5°.

The choice of scale cuts is explored, showing a clear cut-off at θ = 1° for the bias parameter α−1, with increasing θmin beyond this cut-off biasing α, especially at low redshift.

The analysis is robust with respect to Redshift Space Distortions (RSD); the template nuisance parameters compensate for RSD effects, and the relative difference ∆α/α averaged over all redshift bins is 0.25%. Furthermore, the analysis shows no significant bias when a synthetic data vector is used. The constraints are also robust against excluding individual redshift bins; however, excluding bin 11 (zeff = 1.245) decreases α by 1σall bins, highlighting its importance due to its high redshift and small photometric redshift scatter.

Conclusion

The work successfully estimates the ability to constrain cosmological parameters using the Euclid photometric sample through a BAO analysis of galaxy clustering in configuration space. The joint analysis achieves a detection level of ∆det = 10.3σ, representing a three-fold improvement over DES Y6 results, and yields tight constraints on h, omegab, and omegacdm that are consistent with the Flagship simulation cosmology. The study concludes that while optimization of redshift binning is beneficial for future work, the current setup provides strong cosmological constraints.

Key Results Summary:

  1. Joint BAO measurement: α = 1.0011+0.

Improvements for AI systems

As a fastidious and diligent researcher, I have analyzed this paper from the perspective of extracting maximum scientific utility for advanced Artificial Intelligence systems. The core contribution is the rigorous application of Baryon Acoustic Oscillation (BAO) analysis to photometric galaxy clustering data from Euclid simulations.

Here are the specific improvements that can be made to AI systems, categorized by their potential application:

)

The improved AI system can perform high-precision cosmological parameter inference and robust systematic error quantification for large-scale structure surveys. Specifically, it can:

  1. Perform state-of-the-art cosmological parameter estimation (constraining the reduced Hubble constant, baryon density parameter, and cold dark matter density parameter) with a significant improvement over current Dark Energy Survey (DES) constraints at effective redshift 0.77 (improving precision by a factor of three).

  2. Quantify the systematic impact of various analysis choices—such as fitting templates (polynomial orders), scale cuts, redshift binning schemes (equidistant vs. equipopulated), and nuisance parameters like redshift-space distortions (RSD)—on the final cosmological constraints with high fidelity.

  3. Develop an automated framework for analyzing photometric galaxy clustering data by utilizing tomographic approaches to extract BAO signals from angular correlation functions, even when only photometric redshifts are available, leveraging the power of large mock catalogs (like Flagship simulations).

)

The improved AI system can perform state-of-the-art cosmological parameter inference and robust systematic error quantification for large-scale structure surveys. Specifically, it can:

)

The improved AI system can perform state-of-the-art cosmological parameter estimation (constraining the reduced Hubble constant, baryon density parameter, and cold dark matter density parameter) with a significant improvement over current Dark Energy Survey (DES) constraints at effective redshift 0.77 (improving precision by a factor of three).

  1. Quantify the systematic impact of various analysis choices—such as fitting templates (polynomial orders), scale cuts, redshift binning schemes (equidistant vs. equipopulated), and nuisance parameters like redshift-space distortions (RSD)—on the final cosmological constraints with high fidelity.

  2. Develop an automated framework for analyzing photometric galaxy clustering data by utilizing tomographic approaches to extract BAO signals from angular correlation functions, even when only photometric redshifts are available, leveraging the power of large mock catalogs (like Flagship simulations).

Abstract

With about 1.5 billion galaxies expected to be observed, the very large number of objects in the Euclid photometric survey will allow for precise studies of galaxy clustering from a single survey, over a large range of redshifts 0.2 < z < 2.5. In this work, we use photometric redshifts to extract the baryon acoustic oscillation signal (BAO) from the Flagship galaxy mock catalogue with a tomographic approach to constrain the evolution of the Universe and infer its cosmological parameters. We measured the two-point angular correlation function in 13 redshift bins. A template-fitting approach was applied to the measurement to extract the shift of the BAO peak through the transverse Alcock-Paczynski parameter α. A joint analysis of all redshift bins was performed to constrain α at the effective redshift z eff=0.77 with MCMC and profile likelihood techniques. We also extracted one α i parameter per redshift bin to quantify its evolution as a function of time. From these 13 α i, which are directly proportional to the ratio D A/r d, we constrain the product h,r d and Ω m. From the joint analysis, we constrain D A/r d=10.764+0.0839-0.0849, a three-fold improvement over current constraints from the Dark Energy Survey. As expected, the constraining power in the analysis of each redshift bin is lower, with an uncertainty ranging from plus or minus,1.23 to plus or minus,0.289. From these results, we constrain Ω m=0.296+0.074-0.059 and h,r d=99.35+4.29-4.55, Mpc. We quantify the influence of analysis choices such as the template, scale cuts, redshift bins, and systematic effects such as redshift-space distortions, over our constraints, both at the level of the extracted α i parameters and at the level of cosmological inference.

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