Dynamic Zoom Simulations of structure formation beyond standard cosmology

Enrico Garaldi; Federico Marinacci; Marco Baldi; Riccardo Zangarelli

REVIEW 2 major objections 6 minor 75 references

Dynamic Zoom Simulations of structure formation beyond standard cosmology

T0 review · 2 major / 6 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read Dynamic Zoom Simulations — merging particles outside the observer's past lightcone into coarse tracers — are shown to reproduce lightcone observables to about 0.1% accuracy and save up to ~50% runtime in modified-gravity and dark-scattering

desk verdict Useful, honest port of DZS to f(R) and dark-scattering codes, with transparent validation; the MG-F5 accuracy caveat is real but disclosed. read the letter →

arxiv 2602.06133 v2 pith:6OVUKNZP submitted 2026-02-05 astro-ph.CO

Riccardo Zangarelli , Marco Baldi , Federico Marinacci , Enrico Garaldi This is my paper · ORCID

classification astro-ph.CO

keywords DynamicZoomSimulationslightconeoutputmodifiedgravityf(R)darkscatteringN-bodycomputationalperformancestructureformationweaklensing

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper generalizes Dynamic Zoom Simulations (DZS), a scheme that progressively merges particles outside the observer's past lightcone into more massive tracers, from standard ΛCDM N-body runs to two codes implementing non-standard physics: f(R) modified gravity and dark-sector scattering. The central claim is that this outside-lightcone derefinement leaves lightcone observables essentially untouched: lightcone halo mass functions, sky-projected mass maps, matter angular power spectra, and weak-lensing convergence spectra agree with full-resolution runs at around 0.1% or better in most configurations. Runtime savings reach about 50% in the largest validation boxes, and rescaled estimates for state-of-the-art volumes suggest roughly 65–75% savings. If the accuracy holds, DZS makes large, high-resolution simulations of alternative cosmologies affordable enough to support the interpretation of forthcoming survey data.

What carries the argument

The central mechanism is oct-tree derefinement: on each global timestep, a tree walk flags tree nodes outside the lightcone that satisfy the geometric criterion L/(|s| - (R_lc + b)) < θ_geom, then replaces the node's particle content with a single merged 'fictitious' particle carrying the node's mass, center of mass, and center-of-mass velocity. Nodes are merged only up to a maximum size L_max = 4 r_mean, so the external large-scale gravitational field is preserved at a resolution at most 64 times coarser. The algorithm rides on the existing treePM gravity solver without modifying it, and in the f(R) implementation the same oct-tree serves as the adaptive multi-grid for solving the scalar-fi

What would settle it

Run an MG-F5 (strong f(R)) twin pair at survey-grade resolution — particle mass near 10^9 M_sun/h — and compare the high-mass end of the lightcone halo mass function and the l ≳ 1000 weak-lensing convergence power: if deviations exceed the ~0.1–1% range, or the ~2% tail seen in the paper's own MG-F5 case grows, the central claim fails. A more direct check is to compute the f(R) acceleration on identical particles with and without DZS and verify that the per-particle differences are within the force solver's own tolerance.

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Extended reading notes

Core claim

The paper demonstrates that DZS is not tied to ΛCDM: when particles outside the lightcone are merged using the oct-tree, the resulting simulations reproduce the full-resolution lightcone halo mass function, projected mass maps, matter angular power spectrum, and weak-lensing convergence spectrum to ~0.1% or better in most tested configurations, while saving up to ~50% of runtime in the largest validation boxes and an estimated ~65–75% in rescaled state-of-the-art setups. The largest deviations appear in the f(R) model with |f_R0| = 10^-5, where the node-level modified-gravity force responds to tiny DZS-induced particle displacements; even there, halo counts differ by at most ~2% at the highe

Load-bearing premise

The load-bearing premise is that merging particles outside the lightcone does not systematically bias the modified-gravity force computed on the oct-tree's multi-grid cells; if it does at a level above ~0.1%, the headline accuracy claim for beyond-ΛCDM runs would need qualification.

Editorial extensions

If this is right

If DZS holds at the claimed accuracy, large Gpc-scale simulations of f(R) gravity and dark-scattering cosmologies become tractable at state-of-the-art resolution, including model-comparison suites that were previously prohibitive.
The ~0.1% accuracy level sits well below the ~1% target of next-generation weak-lensing surveys, so DZS-generated lightcones can be used to build mock catalogs for pipeline validation and model discrimination.
Runtime savings grow with volume and resolution and are largest for the most expensive solvers: up to ~53% for strong f(R) in an 8192 cMpc/h box, with rescaled estimates of ~65–75% for flagship-like volumes.
Because the algorithm requires no modification to the N-body solver and its own operations add only ~0.1% overhead, it is a generic add-on for any treePM code that produces lightcone output.
Physical differences between cosmologies — including the f(R) power boost and dark-scattering suppression patterns — survive DZS at percent level, allowing the technique to be used for actual model comparison rather than only for single-model production runs.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural but untested extension is DZS with baryonic hydrodynamics: merging particles would destroy gas content outside the lightcone, so a practical implementation would need to carry coarse baryon fields or restrict merging to collisionless components, and the accuracy trade-off is unknown.
A concrete mitigation suggested by the paper's own node-level sensitivity discussion: freeze or smooth the multi-grid cell hierarchy outside the lightcone before merging particles, or compute f_R accelerations on a fixed coarse grid; this could remove most of the observed ~2% high-mass tail while keeping most of the speedup.
A caution for survey use: since DZS accuracy improves with resolution in some models but not in others (the paper notes no worsening, but no consistent improvement in MG-F5 and DS-THAW), the safest validation strategy is to run twin DZS/full simulations at the target resolution for each model rather than interpolating from lower-resolution tests.
A further optimization suggested by the workload-balance analysis: dynamic repartitioning or mid-run changes in the number of tasks could convert some of the observed 1.5–3x imbalances into additional savings, potentially pushing real gains beyond the reported ~50%.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know this is a methods paper that does what it says: it implements Dynamic Zoom Simulations in MG-Arepo and PANDA-Gadget4, adds lightcone output to MG-Arepo, and benchmarks directly against twin standard runs. The DZS idea itself is from Garaldi et al. (2020); the new content is the port to beyond-ΛCDM codes and the validation across four box sizes, two f(R) strengths, and two dark-scattering models. That is a solid, needed extension. Most observables agree to ~0.1% or better, and the runtime savings of up to ~50% are measured, not guessed. The scaling to flagship resolutions is clearly labeled as approximate. The paper is also unusually honest about its own soft spots. Section 3.2 explicitly explains why MG-F5 is the worst case: the f(R) force is computed on multigrid cells built from tree nodes, and tiny DZS-induced displacements can move particles across node boundaries and change the MG contribution. The consequences are visible: up to ~2% in the high-mass halo mass function, ~1% in the convergence power spectrum, and 0.9% of sky pixels above 1% in the massmaps. The stress-test concern about node-level force sensitivity is therefore legitimate. Just as important, the authors note that for MG-F5 and DS-THAW the differences do not improve from medium to mediumHR; they do not get worse, but they do not converge away. So the abstract's '~0.1% in most cases' should be read with that qualifier, and the authors do qualify it in the body. The main missing pieces are typical for this type of work: no released code or data, PANDA-Gadget4 is in preparation, the LCHMF has no error bars, and the high-resolution performance estimate relies on a rescaled lightcone in a small box, for ΛCDM only. The workload balance analysis in Appendix B is a useful addition and shows peaks of 2–3 for MG-F5 mediumHR, which they flag as an opportunity for optimization. Overall, the central claim holds up with caveats. This is not a ground-breaking result, but it is a careful, reproducible-in-spirit engineering contribution that the community will want to use. I would send it to a serious referee.

Referee Report

2 major / 6 minor

Summary. The paper presents implementations of the Dynamic Zoom Simulations (DZS) technique in two codes beyond ΛCDM: MG-Arepo for f(R) gravity and PANDA-Gadget4 for dark-sector scattering. The method derefines the simulation outside the observer's past lightcone to save computational cost. The authors validate accuracy by comparing twin simulations with and without DZS across four box/resolution configurations and five cosmological models, finding that most lightcone halo mass functions, sky-projected mass maps, matter angular power spectra, and weak-lensing convergence power spectra agree to about 0.1% or better, with the MG-F5 model showing larger deviations (up to ~2% in the high-mass LCHMF, ~1% in the convergence spectrum, and >1% in 0.9% of map pixels). Runtime savings in the test suite reach ~50%, and a rescaled-lightcone estimate suggests up to ~75% savings at flagship-like resolutions.

Significance. If fully established, the result is significant: it would extend a proven computational acceleration technique from ΛCDM to two classes of non-standard cosmologies, enabling larger or more numerous simulations for survey interpretation. The validation design is methodologically sound: the comparison is against independent twin standard runs, and the DZS control parameters are inherited from prior work rather than tuned on these runs. The authors are also transparent about the MG-F5 node-level effect and about the approximate nature of the high-resolution extrapolation. The principal limitation is that the f(R) implementation carries a systematic that is not controlled by the usual DZS accuracy parameters, so the headline '0.1%' claim needs to be qualified for the strongest modified-gravity case.

major comments (2)

[§3.2, Figs. 5, 7, 9; abstract] The central accuracy claim is overstated for the f(R) implementation. In the MG-F5 model, 0.9% of sky pixels show >1% relative deviations, the weak-lensing C_kappa(l) reaches ~1%, and the high-mass LCHMF shows ~2% deviations — all larger than the abstract's '≃0.1% or higher'. The paper explains (§3.2) that the MG contribution is computed at node level and that tiny DZS-induced displacements can change particle-to-node assignment, altering particle-level MG accelerations. This is a systematic that the DZS control parameters (θ_geom, b, L_max) do not govern, since those parameters control tree-force accuracy, not the multi-grid node assignment. The authors should provide either a direct comparison of the MG acceleration field between dzs and std runs inside the lightcone, or an explicit MG-specific error budget. The resolution comparison (medium vs mediumHR) shows no improvement for MG-F5,
[§3.1, Fig. 4] The LCHMF relative-difference panels have no error bars. The paper states that the ~2% MG-F5 deviations occur 'at the highest masses where only a handful of halos are detected'. Without Poisson uncertainties on the halo counts, the reader cannot distinguish a genuine systematic DZS bias from small-number statistics. This is load-bearing because the paper itself suggests that 'a larger halo statistics might very well improve this result'. The authors should add Poisson (or jackknife) error bars to the N_LC ratios, or otherwise quantify the statistical uncertainty, so that the MG-F5 accuracy statement is not ambiguous.

minor comments (6)

[Abstract and §5] The phrase 'accuracy of ≃0.1% or higher' is ambiguous. It should be reworded to something like 'accuracy of ≃0.1% or better in most observables' with explicit exceptions noted.
[§3.4] The text says DZS 'only operates at redshift ≲0.69', but Table 1 gives the lightcone entry redshift for the medium box as ~0.36. One of these is a typo; please correct.
[§3.1, Fig. 4 caption] The caption refers to 'the middle left panel of Fig. 3' when discussing the MG-F5 LCHMF; the relevant panels are in Fig. 4, not Fig. 3.
[§3.2, Fig. 3] The relative-difference panels in Fig. 3 use an 'arbitrarily set' y-axis scale. Please use a consistent scale across panels so the reader can compare the magnitude of deviations across models and resolutions.
[§4] The rescaled-lightcone performance estimate is clearly labeled as approximate, but it would help to state explicitly that the rescaling changes the relative size of the lightcone while keeping the density field of the 100 cMpc/h box, so the estimate does not capture large-scale-mode effects on time-stepping or workload imbalance. This is already implied, but should be stated as a formal limitation.
[General] No code or data availability statement is provided. Given that Arepo is a developer version and PANDA-Gadget4 is 'in preparation', a statement on what can be released would strengthen reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the DZS accuracy claim rests on direct comparison with twin standard runs, not on fitted inputs or self-referential definitions.

full rationale

The central accuracy claim is established by running paired 'std' and 'dzs' simulations from identical initial conditions and comparing lightcone observables (LCHMF, massmaps, C(l), C_kappa(l)); this is an external, twin-run benchmark rather than a prediction derived from fitted parameters. The DZS control parameters (theta_geom=0.1, b=5 r_mean, L_max=4 r_mean) are inherited from Garaldi et al. (2020), whose author list overlaps with the present work, but they are not fitted to the validation data here and the accuracy is re-measured against independent std runs, so this self-citation is not load-bearing. The high-resolution performance gain estimate in Section 4 is explicitly described as 'approximate' and based on rescaled-lightcone simulations, not presented as a derived theorem. The MG-F5 node-level sensitivity of the f(R) force is acknowledged in Section 3.2 as a source of percent-level differences; this is an honest limitation and a correctness/accuracy concern, not a circular reduction. No step in the paper reduces to its input by construction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced; merged outside-lightcone particles are numerical tracers, not new physics. The free parameters are the three DZS control knobs inherited from earlier work and chosen without fitting to the validation data. The axioms are standard numerical-cosmology assumptions plus the DZS-specific gravitational-field preservation premise.

free parameters (3)

DZS derefinement threshold θ_geom = 0.1
User-defined opening-angle criterion in Eq. (5); inherited from Garaldi et al. (2020) defaults, not fitted to data. Controls the accuracy/performance trade-off.
DZS buffer length b = 5 r_mean
User-defined buffer radius beyond the lightcone kept at full resolution; set to five mean interparticle separations. Inherited default, not fitted here.
DZS maximum derefinable node size L_max = 4 r_mean
Maximum linear size of a node eligible for derefinement; regulates the minimum resolution outside the lightcone and thus the accuracy of the large-scale gravitational field. Sets the mass resolution floor at 64× coarser than the initial resolution.

assumptions (4)

domain assumption Newtonian gravity with instantaneous force propagation is a valid approximation for cosmological LSS simulations.
Invoked in Section 2, footnote 1 (citing Chisari & Zaldarriaga 2011). DZS relies on this: particles outside the lightcone continue to affect the inside gravitationally, so merging them into low-resolution tracers is a controlled approximation.
domain assumption The Hu-Sawicki f(R) model is parametrized by fR0 with n=1 and its MG force is computed on the oct-tree multi-grid solver inherited from Arnold et al. (2019).
Section 2.1.1. The DZS implementation does not change the MG solver; it assumes the solver remains accurate when the tree structure is modified by derefinement.
domain assumption The dark-scattering momentum-exchange model A(z) of Eq. (4), with the DESI and Lodha et al. w_DE(z) parameterizations, is correctly implemented in PANDA-Gadget4.
Section 2.2.1. The DZS validation compares against the standard run of the same code; it does not independently test the dark-scattering implementation.
ad hoc to paper The DZS derefinement parameters (θ_geom, b, L_max) preserve the large-scale gravitational field sufficiently for sub-0.1% accuracy inside the lightcone.
Section 2.3. This is the core assumption tested by the twin simulations; it is a modeling choice specific to this paper rather than a standard theorem.

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Cite this review

Pith. "Pith review of Dynamic Zoom Simulations of structure formation beyond standard cosmology." pith.science (2026). https://pith.science/paper/6OVUKNZP

@misc{pith2026260206133,
  author       = {Pith},
  title        = {Pith review of: Dynamic Zoom Simulations of structure formation beyond standard cosmology},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6OVUKNZP}},
  note         = {Machine review of arXiv:2602.06133}
}

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 - $\Lambda$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

Figures reproduced from arXiv: 2602.06133 by the authors.

**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 (it is rendered from TNG300-3-Dark simulation data, Nel… view at source ↗

**Figure 2.** Equation of state (EoS) parameter of dark energy wDE as a function of redshift z. The blue curve is the best-fit CPL parametrization from Abdul Karim et al. (2025), with w0 = −0.667, wa = −1.09. Its “phantom” behavior (wDE < −1) at high z is highlighted by the dashed black line, which marks wDE = −1. The orange curve represents a thawing EoS (characterized by wDE → −1 for z → +∞) taken from Lodha et al. (2025, thei… view at source ↗

**Figure 3.** Lightcone halo mass function of the ΛCDM 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. We show the LCHMF for the twin mediumHR ΛCDM simulations in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** 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 ΛCDM std case is overlaid as a dotted line for reference. Relative difference p…

**Figure 5.** Figure 5: Maps showing the angular matter density Σ of the mediumHR twin simulations in the ΛCDM (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 p…

**Figure 6.** Figure 6: Top panel: Angular power spectrum C(l) of ΛCDM mediumHR, medium and largeHR runs. The power is lower in the latter pair of simulations due to the larger output redshift range (see [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: Left column: Angular power spectrum C(l) of the MG-Arepo mediumHR simulations, for the MG-F5 and MG-F6 models (top panel). Solid lines refer to std runs, dashed lines to dzs ones. The ΛCDM std case (dotted line) is overlaid as a reference. Relative difference plots are…

**Figure 8.** Figure 8: Power spectrum boosts, i.e., the ratio C(l)/C(l)ΛCDM, of the mediumHR simulations, for MG models (top panel) and DS ones (bottom panel). Dashed lines at unit boost are shown for reference. ning a higher-resolution simulation, could yield improved (or, at worst, simila…

**Figure 9.** Figure 9: Weak lensing convergence power spectrum Cκ(l) of the mediumHR simulations, for the MG-F5 and DS-DESI models (top panel). Solid lines refer to std runs, dashed lines to dzs ones. Relative difference plots are included for both MG models (middle and bottom panels), wi…

**Figure 10.** Figure 10: Cumulative wall-clock times twc(a) of each rescaled dzs run of the Lbox = 100 cMpc/h, Npart = 5123 setup as a function of the scale factor a. The times are normalized to the final (total wall-clock) time of an std run with the same setup. The latter simulation is also…

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Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

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, " * write output.state after.block = add.period write newline

ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...

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write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

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