Euclid: An emulator for baryonic effects on the matter bispectrum

TL;DR

This work develops a fast emulator for baryonic effects on the matter bispectrum by combining cosmology rescaling, a physically motivated baryon correction model, and a neural network trained on high-resolution BACCO simulations. The emulator reproduces hydrodynamical effects to about $<2\%$ for the 68\% interval across relevant triangle configurations and scales $k$ up to $\sim 20\,h\mathrm{Mpc}^{-1}$, enabling robust predictions for Euclid-like weak-lensing analyses. Validation against FLAMINGO shows unbiased cosmological inferences when using second- and third-order statistics together, with the joint data vector breaking degeneracies and reducing projection effects. The approach provides a scalable, interpolation-based alternative to expensive hydrodynamical simulations and informs optimal choices for modeling baryonic parameters in non-tomographic and tomographic lensing forecasts.

Abstract

Understanding the impact of baryonic processes such as star formation and active galactic nuclei (AGN) feedback on matter clustering is crucial to ensure precise and unbiased cosmological inference. Most theoretical models of baryonic effects to date focus on two-point statistics, neglecting higher-order contributions. This work develops a fast and accurate emulator for baryonic effects on the matter bispectrum, a key non-Gaussian statistic in the nonlinear regime. We employ high-resolution $N$-body simulations from the BACCO suite and apply a combination of cutting-edge techniques such as cosmology scaling and baryonification to efficiently span a large cosmological and astrophysical parameter space. A deep neural network is trained to emulate baryonic effects on the matter bispectrum measured in simulations, capturing modifications across various scales and redshifts relevant to Euclid. We validate the emulator accuracy and robustness using an analysis of \Euclid mock data, employing predictions from the state-of-the-art FLAMINGO hydrodynamical simulations. The emulator reproduces baryonic suppression in the bispectrum to better than 2$\%$ for the $68\%$ percentile across most triangle configurations for $k \in [0.01, 20]\,\mathrm{i}h\mathrm{Mpc}^{-1}$ and ensures consistency between cosmological posteriors inferred from second- and third-order weak lensing statistics. These results demonstrate that our emulator meets the high-precision requirements of the Euclid mission for at least the first data release and provides reliable forecasts of the cosmological information contained in the small-scale matter bispectrum. This underscores the potential of emulation techniques to bridge the gap between complex baryonic physics and observational data, maximising the scientific output of Euclid.

Figures (18)

• Figure 1: Accuracy of the emulator for baryonic effects on the matter power spectrum. The $y$-axis is defined as $\Delta S(k) = S^\mathrm{emu}/ S^\mathrm{true}-1$, where $S(k)=P_{\rm BCM}(k)/P_{\rm GrO}(k)$. The horizontal dashed lines show the 0.5$\%$ region.
• Figure 2: Accuracy of the emulator for baryonic effects on the matter bispectrum $R(\vec{k})$. The upper two rows show the lower and upper $68\%$ percentiles of $\Delta R(\vec{k})$, and the two lower rows show the lower and upper $95\%$ percentiles of $\Delta R(\vec{k})$. Each column is for a different $k_3$ value, which is by construction larger than $k_2$ and $k_1$ but smaller than $k_1+k_2$. The black circles show the actual location where we have measured $B(k_1,k_2,k_3)$. The background is coloured using a linear interpolation/extrapolation of the percentiles between the measured $k$-values.
• Figure 3: Baryonic effects on $\langle \Map^2 \rangle$ (upper panel) and on $\xi_\kappa$ (lower panel), illustrated by ratios of measurements with baryonic physics to GrO measurements. We show with blue triangles the fiducial FLAMINGO measurements, and the grey shaded area represents the DR1 uncertainty. We overplot with a red dashed line the best-fitting BCM to the flamingofied data vector, found by employing our emulators with fixed cosmological parameters.
• Figure 4: Same as Fig. \ref{['fig:xikappa_Map2_Flamingo']} but for the $\langle \Map^3 \rangle$ statistics. The $x$-axis shows different combinations of $\theta_\mathrm{ap,1}$-$\theta_\mathrm{ap,2}$-$\theta_\mathrm{ap,3}$.
• Figure 5: Posteriors of the cosmological parameters $S_8$, $\Omega_\mathrm{m}$, and $\Omega_\mathrm{b}$, analysing a synthetic DR1 joint data vector of second- and third-order weak lensing statistics. We consider several cases. First, a gravity-only (GrO) data vector was analysed with a GrO model (purple contours). We obtain the black contours when baryonic effects are included in the data vector but not in the model. In orange, we illustrate the constraints we get when all elements of the data vector are excluded where the baryonic data vector deviates by more than $0.4\sigma$ from the GrO data vector. Lastly, we show the results if the model includes baryonic feedback in red and blue, where we fixed the baryon parameters to the truth in the blue case and marginalised over all five parameters for the red. The grey dashed line indicates the underlying D3A cosmology.