Dynamic Zoom Simulations of structure formation beyond standard cosmology

TL;DR

This work extends Dynamic Zoom Simulations (DZS) to beyond-$\Lambda$CDM cosmologies by implementing it in Arepo (f(R) gravity) and Gadget4 (dark scattering) to produce lightcone-like outputs with substantially reduced outside-lightcone resolution. The authors show that DZS preserves key lightcone observables—lightcone halo mass functions, sky-projected mass maps, and matter/weak lensing power spectra—at accuracies around $\approx 0.1\%$, while achieving run-time savings up to $\sim 50\%$ in test runs and potentially higher gains for larger volumes and higher resolutions. Validation across multiple models indicates that non-standard physics signatures (e.g., MG boosts or DS drag terms) are still recoverable within the precision required for Stage-IV surveys like Euclid. The results demonstrate that DZS is a practical, scalable approach to enabling cost-effective, large-scale simulations with state-of-the-art resolution, facilitating robust interpretation of forthcoming observational data across diverse cosmologies.

Abstract

(Abridged) A thorough interpretation of the current and upcoming generation of cosmological observations requires unprecedented large-scale, high-resolution simulations spanning multiple cosmological models and parameters. The realization of these computationally demanding simulations poses a crucial technical challenge. We present beyond - $Λ$CDM implementations of the Dynamic Zoom Simulations (DZS) method, a performance-enhancing technique tailored for large-scale simulations that produce lightcone-like outputs. This approach dynamically decreases the resolution of a simulation in the regions that are not in causal connection with the observer, saving computational resources without directly affecting the physical properties within the lightcone. We implemented the DZS algorithm in two state-of-the-art codes supporting non-standard cosmologies, namely modified $f(R)$ gravity in Arepo and dark sector interactions in Gadget4. We analyzed result accuracy and performance gains across resolution, simulation volume and model by comparing runs performed with and without the DZS algorithm. Our DZS reproduce the lightcone halo mass function, sky-projected massmaps, and matter and weak lensing convergence power spectra with an accuracy of $\simeq$ 0.1% or higher in most cases. In terms of performance, DZS runs in our test simulations can save up to $\sim$ 50% runtime compared to the non-DZS counterparts. A scaling to larger simulated volumes suggests that performance gains could improve by an additional $\sim$ 20% at the resolution levels of current state-of-the-art simulations. The validation of the DZS algorithm in non-standard models demonstrates that this technique can enable cost effective, large-scale ($\gtrsim$ 1 cGpc/h) simulations with state-of-the-art resolution, providing the computational framework needed to constrain and help the interpretation of forthcoming data.

Figures (14)

• Figure 1: 1D+1D space-time diagram illustrating the lightcone-like approach of DZS. An example simulation (a cubic box $8192$ comoving Mpc/h on a side) is depicted from its initial conditions (top) to redshift, or lookback time, zero (bottom). The depicted density field is only included for displaying purposes, and does not match the size of the volume marked on the $x$ axis nelson_illustristng_2019. The observer is placed at redshift zero at the location marked with $O$. The simulation volume is crossed by the lightcone (blue curve) at a time indicated by the dashed black line. Traditional snapshots, or time slices, are taken at the cosmic times highlighted by horizontal colored lines, leading to fixed-time density maps of real simulation volumes, rendered from the TNG300-3-Dark (left) and the medium DZS on the right (see Table \ref{['tab:simulations']} in Section \ref{['sec:validation']}).
• Figure 2: Equation of state (EoS) parameter of dark energy $w_{DE}$ as a function of redshift $z$. The blue curve is the best-fit CPL parametrization from collaboration_desi_2025, with $w_0 = -0.667$, $w_a = -1.09$. Its "phantom" behavior ($w_{DE} < -1$) at high $z$ is highlighted by the dashed black line, which marks $w_{DE} = -1$. The orange curve represents a thawing EoS (characterized by $w_{DE} \rightarrow -1$ for $z \rightarrow + \infty$) taken from lodha_extended_2025, and reproducing the low-$z$ trend of the CPL best-fit without the phantom behavior.
• Figure 3: Lightcone halo mass function of the $\Lambda$CDM mediumHR twin simulations (top). The std solid histogram and the dzs dashed histogram are in excellent agreement. This is also shown by the relative difference plot between the two curves (bottom), where we arbitrarily set the $y$ axis scale.
• Figure 4: Left column: Lightcone halo mass function of the MG-Arepo mediumHR twin simulations, for the MG-F5 and MG-F6 models (top panel). Solid lines refer to std runs, dashed lines to dzs ones. The $\Lambda$CDM std case is overlaid as a dotted line for reference. Relative difference plots are included for both MG models (middle and bottom panels), with a dashed line at $N_{LC}^{dzs}/N_{LC}^{std} - 1 = 0$ for reference. Right column: the same as in the left column, but for the DS-DESI and DS-THAW mediumHR simulations.
• Figure 5: Maps showing the angular matter density $\Sigma$ of the mediumHR twin simulations in the $\Lambda$CDM (left column), the MG-F5 (middle column) and the DS-DESI (right column) cases. For each of the three models, maps for the dzs and std simulations are depicted in the top and middle panel, respectively. At the bottom, the relative differences between the dzs and std cases are shown, with the MG-F5 case employing the color green for differences above $1\%$ in absolute value.