Simulation results suggest that the clearest topological difference between collisionless cold dark matter and self-interacting dark matter appeared in the densest, smallest structures, not across the full simulated box. Around the most massive halo examined, the cold-dark-matter model was about twice as clumpy as the self-interacting model when the density field was smoothed over 0.01 Mpc/h. The genus curves, which summarize the field's topology, differed by as much as about 8σ over the reported high-density thresholds. That result is a comparison inside a numerical model, not a measurement showing that either form of dark matter is favored by observations.
A map of density and shape
The researchers compared five dark-matter simulations: one collisionless CDM model and four self-interacting SIDM models. All five began from the same initial conditions, giving the comparison a common starting point. The run started at redshift 60 and followed a 13.8 Gyr Hubble time in a 48 Mpc/h comoving cube. The setup tracks dark matter only, so the calculation does not include baryonic effects.
To turn particles into a measurable field, the study built a density map using a Delaunay tessellation, then projected it onto a regular grid and applied Gaussian smoothing. It examined both the entire box and smaller boxes centered on halos, each extending to three times the halo's virial radius. The density contrast recorded how far a smoothed region lay above or below the mean, measured in units of the density field's standard deviation.
Genus was the main topological statistic. In plain terms, it tracks the changing shape and connectivity of high- and low-density regions as the threshold is moved through the field. The researchers also used a clump-abundance measure, calculated from the area under the genus curve between volume-fraction thresholds of 1.2 and 2.2. A higher CDM-to-SIDM ratio therefore indicated more clump abundance in CDM within the stated comparison.
The signal appears around halos
At large scales, the method did not produce a decisive separation. The residuals between CDM and SIDM genus curves stayed within 3σ, and the reported comparison found no statistically significant topological difference. The signal was therefore not a broad change visible throughout the full simulated volume.
The contrast emerged after focusing on a halo. At a smoothing scale of 0.01 Mpc/h, CDM had more negative genus values than SIDM across the reported high-density threshold range, with discrepancies reaching about 8σ. For the most massive halo, the clump-abundance ratio was about 2, meaning the CDM field was roughly twice as clumpy by that measure. The analysis does not report an exact confidence interval for this single-halo comparison.
That pattern was tested across a larger matched sample at z=0. It included 338 halos with masses from 10^12 to 10^14 solar masses, matched by mass and spatial position across the five simulations. For the constant-cross-section SIDM models, the CDM-to-SIDM clump ratio grew with halo mass. The model with σ0 = 0.2 cm2 g-1 stayed closer to CDM but remained above unity for the highest-mass halos; in the σ0 = 2 cm2 g-1 case, the ratio rose above about 2 for the most massive objects.
The mass trend was different for a velocity-dependent model. With σ0 = 200 cm2 g-1 and ω = 180 km s-1, its clump-abundance ratio flattened and even fell toward the high-mass end.
Mass, scale and time change the picture
Scale was as important as mass. The strongest deviations appeared at smoothing scales of 0.01 and 0.05 Mpc/h. At 0.01 Mpc/h, the ratio reached about 2.1 for the most massive halos; a difference remained down to roughly 10^12 solar masses and exceeded a factor of two around masses above roughly 10^13 solar masses. Once the smoothing scale reached about 0.1 Mpc/h or larger, no significant difference was detected.
The contrast also weakened at earlier times. A separate z=2 comparison used 220 cross-matched halos from three simulations. For the two SIDM models with the strongest deviations, the ratios were still significantly above 1, but were systematically smaller than at z=0. The analysis does not give exact redshift-specific ratio values.
A useful forecast with important gaps
An observation-like two-dimensional test preserved some of the pattern. After projecting the halo distribution into two dimensions, CDM showed larger positive genus values at high density than SIDM, with the clearest contrast for the constant-cross-section model. But the signal was noisier because the halo catalogue provided fewer tracers than the underlying three-dimensional density field. Because it used simulated halo distributions, this was not a direct test of observed galaxies.
The evidence remains limited to the described dark-matter-only numerical setup. The supplied analysis describes one 48 Mpc/h volume rather than multiple independent cosmological realizations, and the mapping from simulated halos to observed galaxies was not validated with observational data. It also reports no formal power calculation, exact p-value, or exact per-bin confidence interval. The study shows where a signal appears in these simulations, not whether a real survey could reliably distinguish the models.
The manuscript is a preprint: its front matter identifies an arXiv version and says it was submitted to A&A. The authors state that the underlying data are available through reasonable request to the authors.
Paper data and sources
Original title: Distinguishing cold and self-interacting dark matter through topological analysis
Authors: Adrian Szpilfidel, Clotilde Laigle, Pierre Boldrini et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
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