Cosmology Likelihood for Observables in \Euclid (CLOE). 1. Theoretical recipe

TL;DR

CLOE is a dedicated cosmology likelihood framework for Euclid that delivers theory predictions and likelihoods for both photometric and spectroscopic probes. It offers a unified treatment of 3×2pt observables in harmonic and configuration space, incorporating a wide array of systematics (IA, baryons, redshift errors, biases) and extensions beyond standard GR. The paper lays out the theoretical recipe, including weighting kernels, pseudo-C_l corrections, BNT scale separation, and EFT-based spectroscopic modelling, setting the stage for robust parameter inference and self-consistent cross-probe analyses. This work serves as the foundation for the subsequent papers in the CLOE series, detailing the code architecture, forecast validations, and extensions to new physics, with the goal of exploiting next‑generation surveys like Euclid to illuminate dark energy and gravity.

Abstract

As the statistical precision of cosmological measurements increases, the accuracy of the theoretical description of these measurements needs to increase correspondingly in order to infer the underlying cosmology that governs the Universe. To this end, we have created the Cosmology Likelihood for Observables in Euclid (CLOE), which is a novel cosmological parameter inference pipeline developed within the Euclid Consortium to translate measurements and covariances into cosmological parameter constraints. In this first in a series of six papers, we describe the theoretical recipe of this code for the Euclid primary probes. These probes are composed of the photometric 3x2pt observables of cosmic shear, galaxy-galaxy lensing, and galaxy clustering, along with spectroscopic galaxy clustering. We provide this description in both Fourier and configuration space for standard and extended summary statistics, including the wide range of systematic uncertainties that affect them. This includes systematic uncertainties such as intrinsic galaxy alignments, baryonic feedback, photometric and spectroscopic redshift uncertainties, shear calibration uncertainties, sample impurities, photometric and spectroscopic galaxy biases, as well as magnification bias. The theoretical descriptions are further able to accommodate both Gaussian and non-Gaussian likelihoods and extended cosmologies with non-zero curvature, massive neutrinos, evolving dark energy, and simple forms of modified gravity. These theoretical descriptions that underpin CLOE will form a crucial component in revealing the true nature of the Universe with next-generation cosmological surveys such as Euclid.

Figures (10)

• Figure 1: Normalised galaxy distribution for each of the 13 baseline tomographic bins extracted from the Flagship simulation (Sect. \ref{['sec:redshift_distribution']}). Each bin has a number density of $1.8674$ galaxies/arcmin$^2$.
• Figure 2: Shear (top left), magnification (top right), and galaxy (bottom) kernels for the 3×2pt harmonic power spectra for the case with 13 equipopulated redshift bins. For increased clarity, we show the kernels for three representative bins only. We do not separately show the IA kernel since it equivalent to the galaxy kernel given our use of the same galaxy sample for both lenses and sources and the absence of photometric RSD.
• Figure 3: Position-position (top), shear-shear (centre), and shear-position (bottom) harmonic power spectra for representative autocorrelation bins. Dashed and solid lines refer to the use of linear and nonlinear ( HMCode2020) matter power spectra, respectively, as input.
• Figure 4: Left. WL harmonic power spectra for three representative autocorrelations with (solid) and without (dashed) IA contributions. Right. Total IA harmonic power spectra for the same bin combinations as in the left panel.
• Figure 5: Left. GCph harmonic power spectra for three representative autocorrelations with (solid) and without (dashed) the magnification contributions. Right. Total magnification harmonic power spectra for the same bin combinations as in the left panel.