Euclid preparation. Cosmology Likelihood for Observables in Euclid (CLOE). 5. Extensions beyond the standard modelling of theoretical probes and systematic effects

TL;DR

Euclid CLOE is extended to test cosmologies beyond LCDM by incorporating magnification bias in spectroscopic clustering, Weyl-potential modifications for gravity, and a consistent massive-neutrino treatment in photometric probes. The authors develop a Weyl-matter conversion framework via $P_{\Upsilon\Upsilon}(k,z)=\Gamma^2(z)P_m^{NL}(k,z)$ with $\Gamma(k,z)=\frac{3H_0^2\Omega_{m,0}}{2c^2}(1+z)\Sigma_{mg}(k,z)$ and implement a two-parameter MG model ($\mu_{mg},\Sigma_{mg}$) tested against fiducial cases, including an integration with MG solver outputs. Validation against external codes and synthetic forecasts shows that including these extensions recovers fiducial cosmologies and that neglecting them can bias key parameters by up to $\sim$0.4–0.7$\,\sigma$, underscoring the necessity of such relativistic and MG effects in precision cosmology. The work also discusses future directions, such as cosmology emulators and simulation-based inference, to speed up and stabilize analyses with CLOE for the coming era of high-precision Euclid data.

Abstract

Euclid is expected to establish new state-of-the-art constraints on extensions beyond the standard LCDM cosmological model by measuring the positions and shapes of billions of galaxies. Specifically, its goal is to shed light on the nature of dark matter and dark energy. Achieving this requires developing and validating advanced statistical tools and theoretical prediction software capable of testing extensions of the LCDM model. In this work, we describe how the Euclid likelihood pipeline, Cosmology Likelihood for Observables in Euclid (CLOE), has been extended to accommodate alternative cosmological models and to refine the theoretical modelling of Euclid primary probes. In particular, we detail modifications made to CLOE to incorporate the magnification bias term into the spectroscopic two-point correlation function of galaxy clustering. Additionally, we explain the adaptations made to CLOE's implementation of Euclid primary photometric probes to account for massive neutrinos and modified gravity extensions. Finally, we present the validation of these CLOE modifications through dedicated forecasts on synthetic Euclid-like data by sampling the full posterior distribution and comparing with the results of previous literature. In conclusion, we have identified in this work several functionalities with regards to beyond-LCDM modelling that could be further improved within CLOE, and outline potential research directions to enhance pipeline efficiency and flexibility through novel inference and machine learning techniques.

Figures (11)

• Figure 1: Relative percentage differences between the $\xi^{\rm g\mu}$ contribution as calculated by CLOE and , for the monopole (blue), quadrupole (green), and hexadecapole (orange) at the four mean redshifts. The grey dotted line denotes equality (zero per cent difference).
• Figure 2: Relative percentage differences between the $\xi^{\mu\mu}$ contribution as calculated by CLOE and , for the monopole (blue), quadrupole (green), and hexadecapole (orange) at the four mean redshifts. The grey dotted line denotes equality (zero per cent difference).
• Figure 3: One- and two-dimensional marginalised posteriors of the cosmological parameters when magnification bias is taken into account within the theoretical modelling of the multipole 2PCF $\xi_{\rm{obs},\ell}(s)$ in CLOE (solid contours, light blue) versus when it is not (dotted contours, dark blue). The fiducial values are denoted by the dotted grey lines.
• Figure 4: Angular power spectra of WL (left), XC (middle), and GCph (right) at fiducial values of parameters of \ref{['tab:w0waCDM']} across different redshift bins (upper panels), and the relative percentage differences between the cases where use_Weyl flag is set to True and False (lower panels).
• Figure 5: Comparison of the one- and two-dimensional marginalised posterior distributions of a subset of cosmological parameters in model for the 3×2pt and WL analyses. Dashed lines and contours correspond to results with the use_Weyl flag enabled, while solid lines and contours show results with the use_Weyl flag disabled.