Euclid preparation. Cosmology Likelihood for Observables in Euclid (CLOE). 4: Validation and Performance

TL;DR

This study validates the Cosmology Likelihood for Observables in Euclid (CLOE) by benchmarking its photometric and spectroscopic predictions against external codes across a broad set of cosmological scenarios and nuisance settings. Using SMAPE for intermediate quantities and a covariance-based χ^2 framework for observables, CLOE consistently achieves agreement at or below the 1% level and within $0.1σ$ of the expected observational errors. The validation covers cosmological functions, 3×2pt observables, and Legendre multipoles, including real-space correlations, demonstrating robust cross-checks between harmonic- and configuration-space representations. The findings support CLOE as a reliable, high-performance tool for Euclid data analysis, minimizing theoretical-bias risks in cosmological inference.

Abstract

The Euclid satellite will provide data on the clustering of galaxies and on the distortion of their measured shapes, which can be used to constrain and test the cosmological model. However, the increase in precision places strong requirements on the accuracy of the theoretical modelling for the observables and of the full analysis pipeline. In this paper, we investigate the accuracy of the calculations performed by the Cosmology Likelihood for Observables in Euclid (CLOE), a software able to handle both the modelling of observables and their fit against observational data for both the photometric and spectroscopic surveys of Euclid, by comparing the output of CLOE with external codes used as benchmark. We perform such a comparison on the quantities entering the calculations of the observables, as well as on the final outputs of these calculations. Our results highlight the high accuracy of CLOE when comparing its calculation against external codes for Euclid observables on an extended range of operative cases. In particular, all the summary statistics of interest always differ less than $0.1\,σ$ from the chosen benchmark, and CLOE predictions are statistically compatible with simulated data obtained from benchmark codes. The same holds for the comparison of correlation function in configuration space for spectroscopic and photometric observables.

Figures (13)

• Figure 1: Summary SMAPE values for the comparison of the cosmological functions as obtained by with those used in . Notice that we only show the transverse distance $f_K(z_1,z_2)$ with $z_2=1$. We obtained the comparison also with $z\in\left[0.5,1.5,2.0\right]$ obtaining the same results. We do not show these to avoid overlapping lines.
• Figure 2: Comparison of the cosmological quantities internally computed by with those extracted from for the cosmologies listed in \ref{['tab:cosmopars']}. Please note that automatically sets $f_K(z_1,z_2)=0$ when $z_1>z_2$, while returns its absolute value for any redshift combination. In order to perform this comparison, we symmetrise the results obtained from . The spikes visible in the comparison of the $f_K(z_1,z_2)$ values are due to this function vanishing when $z_1=z_2$. As in \ref{['fig:cosmo_summary']}, we only show the transverse distance $f_K(z_1,z_2)$ with $z_2=1$, with the other cases showing the same behaviour.
• Figure 3: Summary SMAPE values for the kernels comparison between and in the different cases investigated. Each colour refers to a different redshift bin of the tomographic analysis. The figure shows the comparison result in each case for representative redshift bins at low ($i=1$, black lines), intermediate ($i=7$, orange lines) and high redshift ($i=13$, cyan lines). Notice that for the cases P01 to P06 this latter bin is not available, as the $n(z)$ is divided in only 10 tomographic bins. The specifications of the different cases are reported in \ref{['tab:cases']}.
• Figure 4: Summary comparison for the intermediate power spectra, as computed by and . For each of the different power spectra, shown in separate panels, we show the comparison at different redshifts. The specifications of the different cases are reported in \ref{['tab:cases']}.
• Figure 5: Left panel: distance in units of the expected error for the three photometric observables, both when averaged over the multipoles (solid lines) and taking the highest value of the distance (dashed lines). The black dotted line indicates our threshold of $d=0.1\,\sigma$. Right panel: the solid lines show the average reduced $\chi^2$ value for WL (black), GCph (orange), GGL (cyan), and their combination (green). The dashed lines represent the limiting values of the reduced $\chi^2$ corresponding to the chosen probability threshold. The results are shown for the different cases described in \ref{['tab:cases']}.