The BACCO Simulation Project: Exploiting the full power of large-scale structure for cosmology

TL;DR

The BACCO project addresses the need for precise, scalable predictions of nonlinear structure across cosmologies by combining six high-resolution, large-volume $N$-body simulations with a cosmology-rescaling approach. By reducing the problem to emulating $Q(k,z)=\log[P(k,z)/P_{\rm linear}^{\rm smeared-BAO}(k,z)]$ via PCA plus Gaussian Process and neural networks, the authors achieve $\sim1$–$2\%$ accuracy over $0<z<1.5$ and $10^{-2}<k/(h\,\mathrm{Mpc}^{-1})<5$, across an 8-parameter space that includes dynamical dark energy and massive neutrinos. The emulator is validated against the Euclid code comparison, HaloFit family, and direct N-body results, and demonstrates robust performance beyond minimal $\Lambda$CDM, with potential extensions to include baryonic physics. This framework enables rapid, accurate predictions for cosmological analyses and large-scale structure surveys, supporting precise parameter inference and exploration of beyond-$\Lambda$CDM models. The public availability of the emulator further enhances its impact for the cosmology community.

Abstract

We present the BACCO project, a simulation framework specially designed to provide highly-accurate predictions for the distribution of mass, galaxies, and gas as a function of cosmological parameters. In this paper, we describe our main suite of simulations (L $\sim2$ Gpc and $4320^3$ particles) and present various validation tests. Using a cosmology-rescaling technique, we predict the nonlinear mass power spectrum over the redshift range $0<z<1.5$ and over scales $10^{-2} < k/(h Mpc^{-1} ) < 5$ for 800 points in an 8-dimensional cosmological parameter space. For an efficient interpolation of the results, we build an emulator and compare its predictions against several widely-used methods. Over the whole range of scales considered, we expect our predictions to be accurate at the 2\% level for parameters in the minimal $Λ$ CDM model and to 3\% when extended to dynamical dark energy and massive neutrinos. We make our emulator publicly available under http://www.dipc.org/bacco

Figures (11)

• Figure 1: The projected mass density field in nenya, one of our six BACCO simulations, at $z=0$. Each image corresponds to a $25~ h^{-1}{\rm Mpc}$ deep projection employing a tri-cubic Lagrangian interpolation method. Top, middle, and bottom panels progressively zoom into a $1440\, h^{-1}{\rm Mpc}$, $360\, h^{-1}{\rm Mpc}$, and $90\, h^{-1}{\rm Mpc}$-wide region of the simulation.
• Figure 2: The impact of numerical parameters in our simulated nonlinear mass power spectra at $z=0$ and $z=1$. We display fractional differences with respect to the measurements in a simulation that adopts the same accuracy parameters as our main BACCO simulations. The grey bands indicate a region of $\pm 1\%$.
• Figure 3: The nonlinear mass power spectrum at $z=0$ of the "Euclid code comparison project". Each coloured curve displays the predictions of a different $N$-body code, as indicated by the legend, and we display ratios relative to our simulation result corrected by finite numerical resolution. Note that all $N$-body codes agree to better than $1$% precision up to $k \sim 5 h\,{\rm Mpc}^{-1}$, with the exception of the original Gadget3 run presented in Schneider et al (2016).
• Figure 4: Predictions from the BACCO simulations, vilya, nenya, and narya, at $z=0$. Left panel shows the nonlinear mass power spectrum as solid lines, and linear perturbation theory as dotted lines. The middle panel shows the redshift-space correlation function for subhalos with a number density of $10^{-3}\,h^{3}\,{\rm Mpc}^{-3}$, where solid and dashed lines show the results for each of the two opposite-phase simulations. The right panel shows the Friends-of-Friends halo mass function, with vertical dashed lines indicating the mass limit resolved with 10 and 100 particles.
• Figure 5: Distribution of cosmologies employed to build our BACCO emulator. Blue symbols display the location of cosmologies in our initial training set, whereas orange and green symbols display those subsequently selected by our iterative method. In each plot, the limits coincide with the full range of values considered (c.f. Eq \ref{['eq:par_range']}).