Euclid preparation. Cosmology Likelihood for Observables in Euclid (CLOE). 3. Inference and Forecasts

TL;DR

This paper presents CLOE, a Bayesian inference pipeline for Euclid cosmology, applying nested sampling to synthetic data from weak lensing, angular clustering, galaxy-galaxy lensing, and spectroscopic full-shape measurements. It demonstrates that combining probes via 3×2pt and including GCsp yields dramatic improvements in constraining dark energy via a Figure of Merit exceeding $ FoM \approx 400$ for the flat $w_0w_a$CDM model, and tightens constraints on $S_8$, $n_s$, and $\Omega_m h^2$. The study also reveals non-Gaussian posterior features and projection effects that depend on priors and nuisance treatments, emphasizing the importance of robust systematics modelling and informative priors. Computational demands are substantial, motivating exploration of advanced sampling techniques and data-driven methods to navigate the high-dimensional parameter space efficiently. Overall, the work underscores the power of a full multi-probe, Bayesian approach for Euclid, with significant implications for forecasting precision cosmology ahead of data releases.

Abstract

The Euclid mission aims to measure the positions, shapes, and redshifts of over a billion galaxies to provide unprecedented constraints on the nature of dark matter and dark energy. Achieving this goal requires a continuous reassessment of the mission's scientific performance, particularly in terms of its ability to constrain cosmological parameters, as our understanding of how to model large-scale structure observables improves. In this study, we present the first scientific forecasts using CLOE (Cosmology Likelihood for Observables in Euclid), a dedicated Euclid cosmological pipeline developed to support this endeavour. Using advanced Bayesian inference techniques applied to synthetic Euclid-like data, we sample the posterior distribution of cosmological and nuisance parameters across a variety of cosmological models and Euclid primary probes: cosmic shear, angular photometric galaxy clustering, galaxy-galaxy lensing, and spectroscopic galaxy clustering. We validate the capability of CLOE to produce reliable cosmological forecasts, showcasing Euclid's potential to achieve a figure of merit for the dark energy parameters $w_0$ and $w_a$ exceeding 400 when combining all primary probes. Furthermore, we illustrate the behaviour of the posterior probability distribution of the parameters of interest given different priors and scale cuts. Finally, we emphasise the importance of addressing computational challenges, proposing further exploration of innovative data science techniques to efficiently navigate the Euclid high-dimensional parameter space in upcoming cosmological data releases.

Figures (21)

• Figure 1: Galaxy clustering power spectrum Legendre multipoles, $\pl{k}{\ell}$, as expected from the spectroscopic-survey data within four redshift bins (see values at \ref{['tab:GCspectro_bins']}). The plots show the monopole ($\ell = 0$, dark red dots), quadrupole ($\ell = 2$, blue dots), and hexadecapole ($\ell = 4$, green dots), together with their error bars as given by the corresponding Gaussian covariance matrix. The Poissonian shot noise has been subtracted from the monopole for clarity of plotting.
• Figure 2: Normalised equi-populated photometric galaxy redshift distributions, $n_i(z)/\bar{n}_i$, corresponding to .
• Figure 3: Synthetic harmonic-space weak lensing, $\cl{\ell}[ij][EE]$ (upper triangle) and angular clustering power spectra, $\cl{\ell}[ij][gg]$ (lower triangle), for the auto and cross-correlations between the 13 photometric redshift bins. The shaded error bars show the corresponding uncertainty given by the corresponding analytical covariance matrix. We have used the $C_{\ell}$ notation in the axis labels, as here they refer to the discrete measured power spectra at binned ranges of $\ell$'s.
• Figure 4: Similar to \ref{['fig:CLOE_euclid_probes_WL']} but showing the cross-correlation galaxy-galaxy lensing XC probe$\cl{\ell}[ij][gE]$.
• Figure 5: Heatmap of the logarithm of the Bayes factors ($\ln B$) for different cosmological models relative to (flat), across various probes: Weak Lensing (WL), Galaxy Clustering (GCsp), 3$\times$2pt, and their combination. Darker red shades indicate models strongly disfavoured by the data relative to the reference, while lighter shades indicate models more compatible with the data. The Bayes factor quantifies the relative evidence for each model, automatically penalising unnecessary complexity. Overall, the data generally favour simpler models over extensions such as or models including $\gamma_g$ or curvature. $\ln \evid$ values are found in \ref{['tab:computational_resources']}.