Euclid preparation. Review of forecast constraints on dark energy and modified gravity

The Euclid mission has been designed to provide, as one of its main deliverables, information on the nature of the gravitational interaction, which determines the expansion of the Universe and the formation of structures. Thus, Euclid has the potential to test deviations from general relativity that will allow us to shed light on long-lasting problems in the standard cosmological model, $Λ$CDM. Euclid will mainly do this by using two complementary probes: weak gravitational lensing and galaxy clustering. In this paper we review pre-launch Euclid analyses for dark energy and modified gravity. These include forecast constraints with future Euclid data on cosmological parameters for different cosmological models, such as a time-varying dark energy component, phenomenological modifications of the perturbation sector and specific modified gravity models, with further extensions that include neutrino physics and the coupling to the electromagnetic sector through the fine-structure constant. We review the study of the impact of nonlinear clustering methods on beyond-$Λ$CDM constraints with Euclid. This is of fundamental importance to efficiently predict the large-scale clustering of matter and dark matter halos, given that we will have access to a wealth of information on scales beyond the linear regime. We inspect the extension of theoretical predictions for observable quantities in alternative cosmologies to $Λ$CDM at fully nonlinear scales by means of $N$-body simulations. We discuss the impact of relativistic corrections in extended cosmological models. Overall, this review highlights the significant potential of the Euclid mission to tightly constrain parameters of dark energy and modified gravity models, or perhaps to detect possible signatures of a $Λ$CDM failure.

💡 Research Summary

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This paper is a comprehensive pre‑launch review of the Euclid mission’s capability to constrain dark‑energy (DE) and modified‑gravity (MG) theories. Euclid will obtain an unprecedented spectroscopic and photometric catalogue of billions of galaxies, enabling two primary cosmological probes: weak gravitational lensing (WL) and galaxy clustering (GC). WL measures the integrated effect of the gravitational potentials on light, while GC traces the three‑dimensional distribution of matter through redshift‑space distortions (RSD). The combination of WL, GC, and RSD is emphasized as a powerful way to break degeneracies among cosmological parameters.

The authors organise the forecast studies into two methodological families. The first is a parametric approach, where the dark‑energy equation of state is described by the CPL parametrisation (w₀, wₐ) and MG effects are encoded in the effective Newtonian coupling μ(k,z) and the light‑deflection parameter Σ(k,z). Using Euclid’s expected six‑year survey specifications, Fisher‑matrix analyses predict σ(w₀)≈0.02, σ(wₐ)≈0.07, and sub‑5 % uncertainties on μ and Σ. This approach is computationally cheap and provides intuitive constraints but requires a mapping back to specific theories.

The second family is model‑independent but theory‑driven, based on the Effective Field Theory (EFT) of DE/MG and the Parameterised Post‑Friedmann (PPF) formalism. Within this framework the authors explore a broad spectrum of concrete theories—Horndeski, f(R), Dvali‑Gabadadze‑Porrati (DGP), and Jordan–Brans–Dicke (JBD)—by allowing the scalar‑field mass, kinetic functions, and coupling functions to vary freely. Forecasts are performed in high‑dimensional parameter spaces (10–12 parameters) that also include massive‑neutrino mass Σm_ν, effective number of relativistic species N_eff, and possible variations of the fine‑structure constant Δα/α. The analysis shows that massive neutrinos can mimic MG signatures, leading to degeneracies such as between f_R0 and Σm_ν; multi‑tracer and cross‑correlation techniques are therefore essential.

A major focus of the review is the treatment of non‑linear scales (ℓ ≳ 1000). Standard semi‑analytic prescriptions (HALOFIT, HMcode) calibrated on ΛCDM are shown to be inadequate for MG models, potentially biasing parameter inference. To overcome this, Euclid collaborators have developed dedicated N‑body simulation suites (e.g., ECOSMOG, MG‑GADGET) and machine‑learning emulators (CosmoEmu, Bacco). For f(R) and DGP, simulations achieve ≲0.1 % accuracy on the matter power spectrum, and emulators provide rapid interpolation across the MG parameter space, dramatically reducing the computational cost of Markov Chain Monte Carlo analyses. Baryonic feedback is also incorporated, allowing a realistic assessment of systematic uncertainties on small scales.

The review also addresses relativistic corrections that become important on ultra‑large scales. Effects such as the integrated Sachs‑Wolfe (ISW) contribution, lensing magnification, and Doppler terms modify the observed galaxy number counts in a scale‑ and redshift‑dependent way. Using the PPF framework, the authors derive full‑sky angular power‑spectra that include these corrections and demonstrate that MG models can produce distinctive signatures, especially in the E_G statistic, which combines lensing and velocity information. However, they caution that E_G is sensitive to lensing magnification bias and must be modelled carefully.

Overall, the Euclid mission is projected to improve constraints on DE and MG parameters by factors of 3–5 relative to current Planck, DESI, and BOSS results. In particular, simultaneous constraints on w₀, wₐ, μ, and Σ at the few‑percent level are expected, and the mission will be capable of detecting deviations from General Relativity at the 5 % level or better. The authors stress that achieving these goals hinges on accurate non‑linear modelling, robust inclusion of relativistic effects, and careful treatment of degeneracies with neutrino physics and possible variations of fundamental constants. They conclude that once Euclid data become available, the community will need to iteratively refine theoretical pipelines, validate emulators against high‑resolution simulations, and possibly develop new analysis techniques to fully exploit the mission’s unprecedented statistical power.