Forecast on the generalised dark matter properties from a Euclid-like survey

TL;DR

This work forecasts the ability of a Euclid-like survey to constrain Generalized Dark Matter parameters $w_{ m gdm}$ and $c^2_{s,{ m gdm}}$ by combining GCsp, GCph, WL, and XC. It extends previous forecasts by incorporating nonlinear GDM power spectra from dedicated simulations, updated window functions, IA care, and a full treatment of redshift-space distortions and BAO damping. Across optimistic and pessimistic survey configurations and three $\oldsymbol{\sigma_8}$ normalizations, the results show that single probes leave strong degeneracies, while the complete set of observables enables percent-level constraints on the GDM parameters (about $1.8$–$2.0\%$ in optimistic cases) and robust discrimination between GDM fiducials, highlighting the critical role of cross-correlations and nonlinear modelling for testing beyond-$\Lambda$CDM scenarios. The findings underscore Euclid's potential to address the $\sigma_8$ tension and to decisively test Generalized Dark Matter against standard CDM.

Abstract

The Stage~IV \textit{Euclid} mission will deliver spectroscopic galaxy redshifts together with photometric positions and shapes, enabling cosmological analyses through spectroscopic galaxy clustering (GCsp), photometric galaxy clustering (GCph), weak-lensing cosmic shear (WL), and their cross-correlation (XC). In this work we forecast the constraining power of a Euclid-like survey on the Generalised Dark Matter (GDM) parameters \(w_{\rm gdm}\) and \(c^{2}_{s,{\rm gdm}}\). Our analysis extends previous forecasting pipeline used for standard cold dark matter. For GCsp, we adopt a semi-analytic nonlinear RSD model, with free terms for each bin. For the photometric probes, we compute the nonlinear GDM matter power spectrum using dedicated simulations, and we modify the lensing and clustering window and the intrinsic-alignment prescription. We consider several survey configurations and explore three fiducial values of \(σ_8\) motivated by current CMB and low-redshift measurements. In an optimistic setting, for fiducial values \(σ_8 \simeq 0.81\) and \(σ_8 \simeq 0.77\), we find relative errors of \(4.01\%\) (GCsp), \(5.01\%\) (GCph+WL+XC), and \(1.96\%\) (all probes) on \(c^{2}_{s,{\rm gdm}}\), and \(3.26\%\) (GCph+WL+XC) and \(1.85\%\) (all probes) on \(w_{\rm gdm}\). For a lower fiducial value \(σ_8 \simeq 0.67\), that could strongly disfavor $Λ$GDM, we find constraints of \(5\%\) (GCsp), \(5\%\) (GCph+WL+XC), and \(2.45\%\) (all probes) on \(c^{2}_{s,{\rm gdm}}\), and \(3.43\%\) (GCph+WL+XC) and \(2.04\%\) (all probes) on \(w_{\rm gdm}\). We also found that, combining all probes, whether in the pessimistic or optimistic settings, a Euclid-like survey will be able to disentangle between the three scenarios. These results show that the survey will be able to constrain the GDM parameters and distinguish between normalisations of the matter fluctuations.(Abridged)

Figures (7)

• Figure 1: Showing broad agreement of the GDM model matter power spectrum at linear and nonlinear scales between ones obtained from GDM simulations versus ones following the response approximate method Mead:2016ybv
• Figure 2: Relative differences between the linear matter power spectrum computed with the GDM-class code and our private version, shown at redshifts $z = 0$, $z = 99$, and $z = 127$.
• Figure 3: Relative percent difference in the nonlinear matter power spectrum for $c_{s,{\rm gdm}}^{2}$ varied by $\pm 10\%$ around its fiducial value. The impact is most pronounced at intermediate nonlinear scales, where deviations are maximised.
• Figure 4: Left: 1 and 2$\sigma$ joint marginal error contours on the cosmological parameters for GDM I model from Fisher forecasts in the optimistic settings. In green using spectroscopic Galaxy Clustering (GCsp), in red the photometric probes and their cross-correlations (WL+GCph+XC) and in blue all the photometric probes with their cross correlation combined with spectroscopic Galaxy Clustering (GC$_{\rm sp}$+WL+GCph+XC). Right: 1 and 2$\sigma$ joint marginal error contours on the cosmological parameters for the same model with the same previous probe combinations but in the pessimistic settings.
• Figure 5: Left: 1 and 2$\sigma$ joint marginal error contours on the cosmological parameters for GDM II model from Fisher forecasts in the optimistic settings. In green using spectroscopic Galaxy Clustering (GCsp), in red the photometric probes and their cross-correlations (WL+GCph+XC) and in blue all the photometric probes with their cross correlation combined with spectroscopic Galaxy Clustering (GC$_{\rm sp}$+WL+GCph+XC). Right: 1 and 2$\sigma$ joint marginal error contours on the cosmological parameters for the same model with the same previous probe combinations but in the pessimistic settings.