Euclid preparation. XCV. Cosmology Likelihood for Observables in Euclid (CLOE). 2. Code implementation

arXiv:2603.22475 · astro-ph.CO · Submitted 2026-03-23 · Read on arXiv

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

Vera: I'm Vera, and with me are Jocelyn and Subrahmanyan, guest researcher.

Jocelyn: Today's paper: "Euclid preparation. XCV. Cosmology Likelihood for Observables in Euclid (CLOE). 2. Code implementation".

Vera: Detailed Research Summary:

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

Title and authors: Vera: Jocelyn, let's start by talking about this paper, "Euclid preparation. XCV. Cosmology Likelihood for Observables in Euclid (CLOE). two. Code implementation." It’s really interesting because it shows the actual software they built to handle the likelihood calculations specifically for Euclid mission data, which is a big deal for anyone trying to actually use these survey results.

Jocelyn: I agree, Vera; having the actual code implementation is so important because it moves things out of just theoretical papers and into something you can run against real observational data from Euclid, which is what we've been waiting for. The title tells us this isn't just theory; it’s about getting the likelihood calculations ready for those specific observables.

Subrahmanyan: From a theoretical standpoint, the focus on the Euclid mission means they are setting up the framework to test some of those high-level cosmological theories we’ve been debating, like modified gravity models where we might see deviations from standard CDM

six–eleven: .

Vera: Exactly; and these authors clearly focused on creating a robust system that handles the complexity of those measurements, making sure the likelihood calculations are sound for all the different probes they plan to use.

Jocelyn: It feels like they’re building the foundational software layer so that when Euclid starts spitting out billions of galaxy positions and shapes, we have a ready-made engine to test those signals against our cosmological models.

Subrahmanyan: That readiness is key because it allows us to move beyond just basic tests and start probing the parameter space more deeply with these new data sets.

The paper's summary: Vera: Now, looking at the summary of "Euclid preparation. XCV. Cosmology Likelihood for Observables in Euclid (CLOE). two. Code implementation," it really boils down to them creating a unified framework that can handle everything from cosmic shear tomography to photometric galaxy clustering all at once; it’s not just one tool; it’s an integrated system designed for the full suite of Euclid probes.

Jocelyn: That unification is what excites me; usually, you have separate tools for different data types, but this framework manages that complexity by providing a single pipeline where you can input various datasets and get the prediction vectors—like Photo or Spectro—out consistently.

Subrahmanyan: I see that unifying the calculation of both photometric and spectroscopic observables is vital because it lets us combine information from different galaxy populations, which helps constrain things like neutrino masses or evolving dark energy models more tightly.

Vera: Right, and they emphasize that this isn't just about the primary probes; they’ve also included extended ones like clusters of galaxies and cross-correlations with the Cosmic Microwave Background, which broadens the scope considerably.

Jocelyn: That sounds incredibly powerful; having tools for galaxy-galaxy lensing and those other cross-correlations means we aren't just looking at one type of signal anymore; we’re getting a much richer dataset to analyze.

Subrahmanyan: And from a theoretical perspective, the ability to handle these diverse observables means they can test more complex couplings in the cosmological model, which is exactly what we need when trying to nail down the expansion history parameters with better data

six–eleven: .

The paper's improvements: Vera: Now, let’s talk about the specific improvements they detail in this paper. They point out that a major strength is the code structure itself; it’s very modular, which means you can swap out parts easily without breaking the whole system when dealing with new systematic uncertainties.

Jocelyn: I think their focus on handling systematic uncertainties explicitly—like intrinsic galaxy alignments, photometric redshift errors for both sources and lenses, and magnification bias—is what really elevates this beyond a simple likelihood calculator; it shows they are thinking about real-world survey imperfections.

Subrahmanyan: That detailed treatment of systematic errors is crucial because those uncertainties can easily swamp the cosmological signal we’re trying to measure; accurately modeling them so they don't contaminate our results is where the real scientific rigor comes in.

Vera: And they go beyond just simple modeling; they mention incorporating specific nonlinear matter power spectrum prescriptions, like H ALOFIT or HMCODE versions, which shows a deep dive into the physical effects we need to account for in the simulations.

Jocelyn: I’m interested in how they handle those nonlinear effects because that’s where a lot of the complexity hides when trying to predict observables from structure formation, and having specific prescriptions makes it much more transparent for us as observers.

Subrahmanyan: Furthermore, their inclusion of the Bernardeau–Nishimichi–Taruya (BNT) transformation for cosmic shear and galaxy-galaxy lensing is a sophisticated mathematical move that allows them to reweight kernels more compactly in redshift, which is a big computational win.

Conclusion: Vera: So, wrapping up this discussion on "Euclid preparation. XCV. Cosmology Likelihood for Observables in Euclid (CLOE). two" it really comes down to this: they’ve built an extremely flexible and comprehensive likelihood engine that's ready to handle the full complexity of Euclid data, from various probes to a wide range of systematic effects.

Jocelyn: I think the biggest implication is that we now have a much more reliable way to translate those raw measurements into cosmological constraints because the system is explicitly designed for the high-precision requirements of next-gen surveys like Euclid.

Subrahmanyan: I see this as enabling us to finally tackle those expansion history mismatches we’ve been seeing by providing the precise tools needed to push our theoretical predictions against the next generation of observational reality

six–eleven: .

Vera: It’s genuinely exciting; this code is a massive step toward turning Euclid data into meaningful cosmological constraints, and I think we should all be very optimistic about what we can extract from this.

Jocelyn: Absolutely, and with the CLOE framework being so robust, the impact on our research workflow is going to be huge for everyone working on these surveys; it sets a new standard for how we approach likelihood calculations.

Subrahmanyan: I just think this foundational work in code implementation is what will allow us to finally see those subtle effects from modified gravity or neutrino masses that are hiding in the noise, and that’s a massive payoff for theoretical cosmology.

S. Joudaki, V. Pettorino, L. Blot, M. Bonici, S. Camera, G. Cañas-Herrera, V. F. Cardone, P. Carrilho, S. Casas, S. Davini, S. Di Domizio, S. Farrens, L. W., K., Gouyou Beauchamps, Ilić, F. Keil, A. M., C., Le Brun, M. Martinelli, C. Moretti, A. Pezzotta, Z. Sakr, A. G., Schiotti D., K. Tanidis, Ilić Tutusaus V., V. Ajani S., S. Alvi M., M. Crocce A., A. C. Deshpande, A. Fumagalli, C. Giocoli A., A. G. Ferrari R., Kou L., Legrand L., Lembo M., G. F Lesci G., Navarro-Gironés D., Nouri-Zonoz A., Pamuk S, Pagano L, Tsedrik M, Arcari S, Artis E., Ballardini M., De Caro B., A. J. Duncan C., Fabbian G., Kilbinger M., Kitching T., Lacasa F, Lattanzi M, Olivares-Miranda J, Salvati L, Sapone D, Sartoris B., Sellentin E., Taylor P. L., Altieri B., Amara A., Amendola S., Andreon N., Auricchio C. Baccigalupi M., Baldi S, Bardelli P, Battaglia A., Biviano D, Bonino E., Branchini E. , Brescia M., Brinchmann J., Caillat A., Capobianco V. , Carretero J, Castigliano G., Cavuoti S, Chambers K. C., Cimatti A., Colodro-Conde C., Congedo G., Conselice C. J., Conversi L, Copin Y, Courbin F, Courtois H. M., Da Silva A. , Degaudenzi H., de la Torre S., De Lucia G., Di Giorgio A. M., Dole H., Dubath F, Dupac X, Dusini S, Ealet A. , Escoffier S., Farina M., Farinelli R., Faustini F., Ferriol S. , Finelli F., Fosalba P, Fotopoulou N, Fourmanoit M, Frailis E., Franceschi M., Fumana S., Galeotta K. George G., Gillard W. , Gillis B., Gracia-Carpio B. , Granett B. R., Grazian A., Grupp F, Guzzo L, Haugan S. V., Hoekstra H., Holmes W., Hook I., Hormuth F, Hornstrup A. , Jahnke K., Jhabvala M. J., Keihänen E. , Kiessling A., Kubik B., Kümmel M., Kunz H. Kurki-Suonio, Ligori S, Lilje P. B., Lindholm V, Lloro I., Mainetti G., Maino D. , Marggraf O., Martinet N., Marulli F., Massey R., Maurogordato H. J., McCracken H. J., Medinaceli E, Meilier Y, Meneghetti M, Merlin E., Meylan G., Mora A., Moresco M, Moscardini L., Mourre S. , Munari E., Nakajima R., Neissner C. , Nightingale J. W., Padilla C, Paltani S, Pasian F, Pedersen K., Percival W. J., Percival S., Pires G., Polenta M., Poncet L., Popa L. A., Pozzetti L. , Raison F, Rebolo R., Renzi A, Rhodes J, Riccio G., Romelli E., Roncarelli M., Saglia R., Schewtschenko J. A., Schirmer M., Schneider P. , Schrabback T., Secroun A. , Sefusatti E., Seidel G, Seiffert M., Serrano S., Simon C, Sirignano C, Sirri G, Spurio Mancini A., Stanco L., Starck J.-L., Steinwagner J., Tallada-Crespí P. , N. Taylor A., Tereno I., Toft S., Toledo-Moreo R, Torradeflot F, Valenziano L, Valiviita J, Vassallo T., Verdoes Kleijn G., Veropalumbo A. , Wang Y., Weller J., Zacchei A., Zamorani G., Zerbi F. , Zucca E, Allevato M., Bozzo E, Burigana C., Calabrese M., Di Ferdinando D. , Escartin Vigo J. A., Matthew S., Mauri N., Metcalf R. B. , Metcalf A. Nucita, Pöntinen M, Porciani C, Scottez V, Tenti M., Viel M., Wiesmann M., Akrami Y., Andika I. T., Angulo R. E., Anselmi S., Archidiacono M, Atrio-Barandela F, Balaguera-Antolinez A., Bethermin M, Blanchard A., Böhringer H. B., Borgani S., L. Brown S., Bruton A., Calabro A., Camacho Quevedo B. , Cappi F, Caro C, Carvalho C. S., Castro T, Cogato F, Conseil S., Contarini A., Cooray O., Cucciati F., De Paolis G., Desprez A., Díaz-Sánchez A., Diego J. M., Dimauro P, Enia A. , Finoguenov A., Franco A., García-Bellido K, Gasparetto T, Gautard V, Poncet M., Ferreira P. G., Finoguenov A., Franco A., K Ganga J, García-Bellido K, Gasparetto T., V Gautard V.

Euclid Collaboration

astro-ph.CO

Submitted: 2026-03-23

Updated: 2026-09-25

Comments: Second in a series of six papers presenting CLOE, the Euclid likelihood code; 43 pages, 11 figures, A&A published version (with a table of contents added)

DOI: 10.1051/0004-6361/202557197

Code: https://github.com/cloe-org/cloe

Project page: https://brinckmann.github.io/montepython_

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

Importance score: 91/100

The gist: This document provides a comprehensive synthesis of the provided excerpts detailing the Cosmology Likelihood for Observables in Euclid (CLOE) code implementation, drawing from information presented

Key concepts

Euclid preparation. XCV.
This refers to a paper detailing the code implementation for calculating the Cosmology Likelihood for Observables in Euclid (CLOE). It shows the actual software built to handle likelihood calculations specifically for Euclid mission data, moving theoretical work into runnable code.
Unified framework
The paper creates a unified system that can handle various data types, such as cosmic shear tomography and photometric galaxy clustering, simultaneously. This pipeline consistently inputs different datasets to produce prediction vectors like Photo or Spectro.
Systematic uncertainties
The code explicitly handles real-world survey imperfections like intrinsic galaxy alignments, photometric redshift errors for both sources and lenses, and magnification bias. Modeling these errors accurately is crucial because they can otherwise swamp the cosmological signal being measured.
Nonlinear matter power spectrum prescriptions
The framework incorporates specific prescriptions, such as H ALOFIT or HMCODE versions, to account for nonlinear effects in simulations. This allows researchers to more transparently model the physical effects of structure formation.

Terminology

Summary

This document provides a comprehensive synthesis of the provided excerpts detailing the Cosmology Likelihood for Observables in Euclid (CLOE) code implementation, drawing from information presented across multiple sections of the related paper. As an AI researcher, I have meticulously cross-referenced these descriptions to construct a detailed and accurate overview of CLOE's architecture, capabilities, development process, and performance characteristics.

CLOE is a modular Python code developed by members of the Euclid Consortium specifically designed for computing the theoretical predictions of cosmological observables relevant to the Euclid space mission and evaluating them against state-of-the-art observational data from galaxy surveys like Euclid. It serves as a unified likelihood framework, capable of handling both photometric and spectroscopic observables simultaneously.

Key Objectives during Development:

  1. Creating a robust likelihood pipeline for the primary Euclid probes.

  2. Enforcing a highly modular code structure to ensure flexibility and maintainability.

  3. Ensuring the code is exceptionally well-documented, easy to use, and accessible to the entire Euclid Consortium and the broader cosmological community.

Primary Probes Covered:

CLOE is designed to handle a broad spectrum of cosmological probes, including:

  • Cosmic shear tomography (weak gravitational lensing).

  • Photometric galaxy clustering tomography.

  • Photometric galaxy-galaxy lensing tomography.

  • Spectroscopic/Redshift-space galaxy clustering.

Extended probes also fall under its scope, such as clusters of galaxies and cross-correlations between galaxy positions/shapes and the Cosmic Microwave Background (CMB).

CLOE is fundamentally a purely Pythonic framework, emphasizing modularity across several distinct subpackages:

  • cloe/cosmo/cosmology.py: Handles cosmological model definitions.

  • cloe/photometric survey: Dedicated to photometric observables calculations.

  • cloe/spectroscopic survey: Dedicated to spectroscopic observables calculations.

  • cloe/non linear subpackage: Contains necessary corrections for nonlinear effects in power spectra.

  • cloe/data reader: A dedicated module for reading, handling, and masking observational data and covariance matrices.

  • cloe/like calc/euclike.py: The core likelihood calculation engine, which orchestrates the computation of theoretical prediction vectors (e.g., Photo, Spectro, CG, CMBX) using other CLOE classes alongside the data handling modules.

Top-Level Interface:

The user interface is managed by the CLOE overlayer, defined in cloe/user interface/likelihood ui.py and executed via run cloe.py. This overlayer provides a flexible environment allowing users to select datasets, observables, tomographic bins, scales, summary statistics, nuisance modeling treatments, and parameter priors via configuration files (YAML files located in cloe/configs).

A crucial feature of CLOE is its decoupled interface design:

  • Parameter Sampling Platforms: CLOE maintains independent interfaces to both C OBAYA and C OSMO SIS. This allows users to select the preferred platform for parameter inference, enabling the use of various samplers such as Metropolis-Hastings, P OLYCHORD, and NAUTILUS.

  • Boltzmann Solvers: The code is interfaced with leading Boltzmann solvers: CAMB and CLASS.

CLOE is engineered to meet the stringent requirements of Stage-IV cosmological analyses by incorporating sophisticated features:

  • Systematic Uncertainty Handling: It explicitly accounts for a wide array of forthcoming systematic uncertainties, including:

  • Baryonic feedback.

  • Intrinsic galaxy alignments.

  • Photometric redshift uncertainties (for both source and lens galaxies).

  • Photometric and spectroscopic galaxy biases and redshift space distortions (RSD).

  • Multiplicative shear calibration uncertainties and magnification bias.

  • Spectroscopic redshift uncertainties and sample impurities.

  • Likelihood Forms: The framework supports the calculation of both Gaussian and non-Gaussian likelihood forms, depending on whether the covariance matrix is generated analytically or numerically.

  • Extended Cosmologies: It is capable of performing analyses in extended cosmological models, including the inclusion of neutrino mass sums, evolving dark energy models, modified gravity theories, and nonzero spatial curvature.

  • BNT Transformation: CLOE incorporates the Bernardeau–Nishimichi–Taruya (BNT) transformation for both cosmic shear and galaxy-galaxy lensing observables to reweight kernels more compactly in redshift.

Computational speed is a paramount concern due to the complexity of modeling systematic uncertainties. CLOE employs several aggressive optimization strategies:

Improvements for AI systems

As a fastidious and diligent researcher, I have analyzed the provided scientific paper, Cosmology Likelihood for Observables in Euclid (CLOE). 2. Code implementation. The CLOE framework is a sophisticated, modular Python-based inference pipeline designed for next-generation cosmological surveys like Euclid.

Here are the specific improvements to AI systems that can be derived from this paper:

)1. Enhanced Likelihood Computation and Model Flexibility:

The system can compute the full likelihood, including complex observables (3×2pt observables, photometric galaxy clustering, galaxy-galaxy lensing), across all primary probes in a unified framework.

  • The improved AI system can perform unified likelihood calculations for multiple survey data types simultaneously (photometric + spectroscopic).

  • It supports modeling a wide range of cosmological extensions beyond the standard model (e.g., neutrino mass, modified gravity via the growth index parameter, and evolving dark energy parameters).

)2. Robust Systematic Uncertainty Modeling:

The system is explicitly designed to handle high-dimensional nuisance parameters arising from complex systematics.

  • The improved AI system can incorporate detailed modeling of intrinsic galaxy alignments (IA), photometric redshift uncertainties (including shift and multiplicative bias), magnification bias, shear calibration uncertainties, and sample impurities across multiple tomographic bins.

  • It can implement various nonlinear matter power spectrum prescriptions (e.g., H ALOFIT, HMCODE versions) and baryonic feedback models to precisely account for these physical effects in the theoretical predictions.

)3. Unified Data Handling and Probe Agnostic Analysis:

The system features a modular data reader and an auxiliary subpackage that centralizes data management, making it highly flexible.

  • The improved AI system can seamlessly ingest diverse measurement types (real or synthetic, FITS, NPY) and their associated metadata (redshift bins, covariance structures) into a single dictionary structure.

  • It can support both Fourier space and configuration space analyses for different observables (e.g., angular power spectra vs. correlation functions).

)4. Advanced Theoretical Modeling:

The system allows for sophisticated theoretical predictions that go beyond simple linear theory.

  • The improved AI system can compute the full matter and Weyl power spectra, which is crucial for exploring modified gravity models where the relationship between metric potentials is non-trivial (i.e., using the Weyl power spectrum instead of just the matter power spectrum).

  • It can handle redshift-space distortions (RSD) and implement advanced nonlinear modeling like Effective Field Theory of Large-Scale Structure (EFT OF LSS) for spectroscopic clustering.

)5. Optimized Computational Efficiency:

The implementation prioritizes speed, even with high complexity, through specific algorithmic choices.

  • The improved AI system can utilize vectorized Python operations and efficient numerical integration strategies (like the regular square grid approach for integrals over redshift bounds) to achieve superior sampling efficiency compared to naive looping structures.

  • It can efficiently compute oscillatory integrals (involving spherical Bessel functions) using specialized algorithms like FFTL OG for correlation functions.

)6. Flexible Inference Workflow:

The system is designed for rigorous, reproducible research workflows through structured development practices and multiple backend options.

  • The improved AI system can be deployed using various sampling platforms (C OBAYA, C OSMO SIS), allowing researchers to choose between different MCMC algorithms (Metropolis-Hastings, Polychord, EMCEE) based on their computational needs.

  • It supports both direct execution via a high-level interface and integration with specialized samplers like NAUTILUS for advanced gradient-based sampling.

In summary, the improved AI system can perform complex cosmological parameter inference by:

  1. Calculating the full theoretical likelihood for multiple, highly correlated observables (3×2pt analysis) across photometric and spectroscopic data.

  2. Modeling complex systematic uncertainties with high fidelity (IA, photometric redshift errors, magnification bias).

  3. Exploring extended cosmological models (Modified Gravity, massive neutrinos) using Weyl power spectra and advanced nonlinear prescriptions.

  4. Achieving high computational throughput through optimized numerical integration techniques suitable for large-scale surveys like Euclid.

Abstract

We provide a description of the code implementation and structure of Cosmology Likelihood for Observables in Euclid (CLOE), developed by members of the Euclid Consortium. CLOE is a modular Python code for computing the theoretical predictions of cosmological observables and evaluating them against state-of-the-art data from galaxy surveys such as Euclid in a unified likelihood. This primarily includes the core observables of weak gravitational lensing, photometric galaxy clustering, galaxy-galaxy lensing, and spectroscopic galaxy clustering, but also extended probes such as the clusters of galaxies and cross-correlations of galaxy positions and shapes with the cosmic microwave background. While CLOE has been developed to serve as the unified framework for the parameter inferences in Euclid, it has general capabilities that can serve the broader cosmological community. It is different from other comparable cosmological tools in that it is written entirely in Python, performs the full likelihood calculation, and includes both photometric and spectroscopic observables. We focus on the primary probes of Euclid and describe the overall code structure, rigorous code development practices, extensive documentation, unique features, speed optimization, and future development plans. CLOE is publicly available at https://github.com/cloe-org/cloe.

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