Euclid preparation. Galaxy power spectrum modelling in redshift space

TL;DR

The paper tackles the challenge of modelling redshift-space distortions in galaxy clustering for Euclid by comparing three one-loop approaches: EFT, VDG$_{\infty}$, and the BACCO emulator. It systematically evaluates each model’s ability to recover cosmological parameters ($h$, $\omega_c$, $A_s$) using mock H$\alpha$ data across four redshift bins, employing robust metrics (FoB, FoM, and p-value) and a thorough analysis of scale cuts up to $k_{\max}$. The main finding is that VDG$_{\infty}$ and BACCO outperform EFT across the scales considered, with BACCO showing saturation at intermediate scales and VDG$_{\infty}$ continuing to improve constraints up to $k_{\max}\approx0.35$–$0.4\,h\,\mathrm{Mpc}^{-1}$, while EFT exhibits biases beyond $k_{\max}\approx0.25\,h\,\mathrm{Mpc}^{-1}$. These results imply that improved small-scale RSD modelling, including damping and higher-order effects, is crucial for exploiting Euclid’s full potential, with BACCO offering the strongest cosmological gains at realistic computational costs.

Abstract

Accurate modelling of redshift-space distortions (RSD) is essential for maximizing the cosmological information extracted from large galaxy redshift surveys. In preparation for the forthcoming analysis of the Euclid spectroscopic data, we investigate three approaches to modelling RSD effects on the power spectrum multipoles of mock H$α$ emission line galaxies. We focus on two one-loop perturbation theory models -- the effective field theory (EFT) and velocity difference generator (${\rm VDG_ \infty}$) -- which differ in their treatment of the real-to-redshift space mapping on small scales, and a third approach, the BACCO emulator, which adopts a hybrid strategy combining perturbation theory with high-resolution N-body simulations. We assess the ability of these models to recover key cosmological parameters, including the expansion rate $h$, the cold dark matter density parameter $ω_{\rm c}$, and the scalar amplitude $A_{\rm s}$, across four redshift bins spanning $0.9 \leq z \leq 1.8$. In each bin, we find that ${\rm VDG_ \infty}$ and BACCO outperform the EFT model across all scales up to $k_{max} \lesssim 0.35 h\,Mpc^{-1} $. While BACCO saturates in constraining power at intermediate scales and higher redshift, the ${\rm VDG_ \infty}$ model continues to improve parameter constraints beyond $k_{max} \gtrsim 0.30 h\,Mpc^{-1}$. The EFT model, although robust on large scales, exhibits significant parameter biases for $k_{max} \gtrsim 0.25 h\,Mpc^{-1}$, limiting its applicability to Euclid-like H$α$ samples. Among the full perturbation theory-based models, the enhanced treatment of small-scale RSD effects in ${\rm VDG_ \infty}$ improves cosmological parameter constraints by up to a factor of two.

Figures (15)

• Figure 1: Power spectrum Legendre multipoles as measured from the Model 3 samples built on the Flagship I comoving snapshots. Markers show each multipole along the $z$ axis, with different colours marking different multipoles as indicated in the legend. The error bars correspond to the Gaussian covariance for a comoving volume corresponding to the full box of the Flagship I simulation, as described in Sect. \ref{['sec:data']}. Dashed red line refers to the Poissonian shot-noise contribution $P_{\rm sn}$. For visualization purposes, we show only one out of three data points.
• Figure 2: Performance metrics -- , , and $p$-value are shown in the top, middle, and bottom row, respectively -- for the two different models, here marked with different colours, as a function of the maximum fitting scale $k_{\rm max}$. For each case, we show the maximal-freedom configuration (dashed lines with circle markers), the minimal-freedom one (dotted lines with triangle markers), and the one with only $\gamma_{21}$ fixed to the coevolution relation (solid lines with diamond markers). In all cases, we assume a covariance matrix matching the full volume of the Flagship comoving snapshots. Each column shows results at different redshift bins. The grey bands in the and $p$-value panels represent the $68\%$ and $95\%$ percentiles of the corresponding distribution.
• Figure 3: Same as in Fig. \ref{['fig:compare_EFTvsVDG_AllFreeAndg2g21Fix']}, but only for the minimal-freedom bias configurations, and showing the impact of different values of $\Delta k$ in the determination of the $k_{\rm max}$ for the quadrupole and hexadecapole.
• Figure 4: Same as in Fig. \ref{['fig:compare_EFTvsVDG_AllFreeAndg2g21Fix']}, but only for the minimal-freedom bias configurations, and showing the impact of different configurations for the shot-noise parameters.
• Figure 5: Performance metrics for the three models presented in Sect. \ref{['sec:theory']} assuming a covariance matrix matching the expected volume by the end of the mission. The and are shown in the first two columns, while the bottom panel shows the relative error of each parameter with respect to its fiducial value, as indicated in the legend. Each column shows results for a different redshift bin. Different colours correspond to different models, as described in the legend. To have a consistent number of degrees of freedom, for the -based models, we adopt the configuration with $\gamma_{21}$ fixed to the co-evolution relation and the anisotropic noise contribution $N_{22}^P$ set to 0. The $x$ axis shows the maximum wave mode $k_{\rm max}$ adopted in the fit. The grey bands in the panel represent the $68\%$ and $95\%$ percentiles of the corresponding distribution, as explained in Sect. \ref{['sec:figure_of_bias']}.