Five cosmological dark-matter simulations have produced a sharp but highly localised distinction between collisionless cold dark matter (CDM) and self-interacting dark matter (SIDM): the difference appeared around halos at the smallest smoothing scale, while the full simulated box showed no statistically significant split. Around the most massive halo, the reported genus discrepancy reached approximately eight standard deviations.
The result comes from a preprint that asks whether the genus statistic can distinguish SIDM from CDM by tracing the topology of a density field—the pattern formed by its high- and low-density regions. The authors compared one collisionless model with four self-interacting models, all started from the same initial conditions.
The clearest split was local
Genus is a way of summarising that pattern as the density threshold changes. The team estimated genus for the full simulation volume and for halo-centred boxes sized at three times the virial radius. To capture clumpiness in one number, it defined the clump-abundance measure AC as the area under the genus curve between thresholds 1.2 and 2.2.
In the large-scale comparison, residuals between the CDM and SIDM curves stayed within 3σ, and no statistically significant topology difference was detected. That makes the scale of the measurement central to the finding: the models looked alike in the broad, full-box view even though they separated in a much finer, halo-centred view.
At RG = 0.01 Mpc/h and thresholds from 1 to 3, the CDM genus was substantially more negative than the SIDM genus. The largest reported discrepancy was approximately 8σ. In ordinary terms, the fine-grained map showed a different balance of dense clumps and surrounding gaps in CDM and SIDM, while smoothing the field over larger distances weakened the contrast.
The answer changed with the model
To see whether the pattern extended beyond one object, the main z = 0 halo analysis examined 338 cross-matched halos with masses from 10¹² to 10¹⁴ M⊙. The regions used Lbox = 3Rvir and RG = 0.01 Mpc/h. The ratio of CDM to SIDM clump abundance rose with halo mass in the constant-cross-section models, exceeding about 2 for the most massive halos in the σ₀ = 2 cm² g⁻¹ case; the σ₀ = 0.2 cm² g⁻¹ model stayed closer to CDM.
The mass trend was not universal across the tested interactions. In the velocity-dependent model with σ₀ = 200 cm² g⁻¹ and ω = 180 km s⁻¹, it flattened and then decreased at high halo mass. The contrast between these cases leaves the signal tied to the interaction prescription as well as to halo size.
Smoothing mattered just as much. At RG = 0.01 Mpc/h, the clump-abundance ratio reached about 2.1 for the most massive halos, and CDM remained significantly clumpier down to roughly 10¹² M⊙. Around 10¹³ M⊙ and above, the discrepancy exceeded a factor of two. Once RG reached roughly 0.1 Mpc/h or more, no significant difference was detected.
The signal was also weaker at the earlier redshift tested. At z = 2, the ratios remained above unity but were systematically smaller than at z = 0, while the mass pattern stayed qualitatively similar: larger halos showed stronger deviations.
A weaker signal in two dimensions
The researchers then built an observation-like version of the test. They projected halo positions into two dimensions, treated each halo as a point, and weighted it by virial mass before estimating the density field. Because this remained a projection of the simulation, it was a test of an observing strategy rather than an observational measurement.
That projected analysis used regions centred on 325 halos for the constant-cross-section σ₀ = 2 cm² g⁻¹ model and 327 halos for the corresponding velocity-dependent model with ω₀ = 180 km s⁻¹. The projected genus retained the qualitative three-dimensional pattern but was noisier. Across 1 ≲ νf ≲ 3, CDM had systematically more positive genus values than SIDM, with the clearest difference in the constant-cross-section case.
Projection also reduced apparent sensitivity. The full three-dimensional analysis reached a clump-abundance ratio of about 2.2 for the most massive halos, whereas the projected deviations were smaller and came with larger uncertainties. A survey built from projected halo positions, in other words, may not recover the full strength of the three-dimensional signal.
A model comparison, not a dark-matter detection
The results point toward a possible observational use, but only as a future test. The signal was strongest around massive, low-redshift halos, while the projected version was weaker and noisier than the full three-dimensional field.
Important caveats remain. This was a comparison of five DM-only simulations with one CDM model and four SIDM models, focused on selected halo-centred regions. It does not provide an observational constraint on dark-matter self-interactions, and the signal has not been shown to survive baryonic physics or real survey effects.
For now, the finding is a guide to where a distinction might be visible: at fine scales around massive halos, in three-dimensional fields, and more clearly at z = 0 than at z = 2. It is not a verdict on which form of dark matter exists.
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
Original paper · Full text