Dynamic Zoom Simulations of structure formation beyond standard cosmology

(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.

💡 Research Summary

The paper addresses a pressing computational bottleneck in modern cosmological simulations: the need to simultaneously cover very large volumes (≥ 1 cGpc/h) and achieve high mass resolution (≲ 10⁹ M⊙/h) while producing light‑cone outputs that match the observational geometry of upcoming surveys such as Euclid, Rubin, DESI, and SKA. Traditional snapshot‑based approaches waste a substantial fraction of CPU time on regions that lie outside the observer’s past light‑cone, especially at low redshift where non‑linear structure formation is most demanding.

To mitigate this inefficiency, the authors extend the Dynamic Zoom Simulations (DZS) technique—originally demonstrated only for ΛCDM dark‑matter‑only runs in Gadget‑3—to two state‑of‑the‑art codes that support non‑standard cosmologies: Arepo (with an f(R) modified‑gravity implementation) and Gadget‑4 (with a dark‑scattering interaction model). DZS works by dynamically lowering the resolution of particles that have crossed the light‑cone, merging them into more massive “super‑particles” while preserving total mass and momentum. Crucially, the method requires only minimal changes to the underlying N‑body solver (primarily the tree construction and traversal logic) and does not alter the periodic boundary conditions, making it broadly applicable.

Implementation details are discussed in depth. In Arepo, the tree‑PM gravity solver is leveraged; the tree nodes store mass and centre‑of‑mass information that DZS uses to decide when and how to merge particles based on distance from the light‑cone and a user‑defined mass threshold. The f(R) scalar field solver (a multigrid‑accelerated Poisson‑type equation) remains untouched, ensuring that the modified‑gravity forces are computed accurately for both high‑ and low‑resolution regions. In Gadget‑4, the dark‑scattering model introduces a velocity‑dependent drag term proportional to the dark‑energy equation‑of‑state parameter w_DE(z). The DZS algorithm is adapted to respect the additional force term by synchronising particle merging with the drag computation, thereby avoiding spurious momentum loss.

The authors validate the method by running paired simulations (with and without DZS) for each cosmology across a range of resolutions and volumes. Key observables—halo mass functions within the light‑cone, sky‑projected mass maps, matter power spectra, and weak‑lensing convergence spectra—are reproduced with relative differences ≤ 0.1 % in almost all cases, well within the statistical uncertainties expected for upcoming surveys. Performance benchmarks show runtime reductions of up to ~50 % for the test suite (a box of 8192 cMpc/h with ~2 × 10⁹ particles). Extrapolating to larger volumes suggests an additional ~20 % gain, as the fraction of low‑resolution volume grows at late times. Memory consumption follows a similar trend, easing I/O and storage demands.

The paper also discusses scalability, showing near‑linear strong scaling up to ~10⁴ MPI ranks, and highlights that the DZS overhead (tree traversal for merging decisions) remains a small fraction of total compute time. The authors argue that because DZS does not interfere with the core gravity solver, it can be combined with other performance‑enhancing strategies (e.g., adaptive time‑stepping, GPU acceleration) without conflict.

In conclusion, the study demonstrates that Dynamic Zoom Simulations can be robustly extended to modified gravity and interacting dark‑energy models, delivering substantial computational savings while maintaining sub‑percent accuracy on all relevant large‑scale‑structure statistics. This opens the door to systematic explorations of beyond‑ΛCDM parameter spaces at resolutions previously deemed prohibitive, thereby providing the essential theoretical backbone for the interpretation of next‑generation cosmological data sets.