Khronon Jeans Fragmentation: Three Dark Matter Morphologies

When the Khronon field's effective sound speed cs → 0 at sub-galactic scales, all Fourier modes become simultaneously Jeans-unstable. Our simulations show this produces filamentary structure — distinct from both wave dark matter (periodic interference) and CDM (discrete subhalos).

Volume rendering — ray marching through a continuous 3D density field. Semi-transparent fog reveals internal filamentary structure and voids. Best for seeing the topology of each model.
Voxel rendering — discrete cubes colored by density. Each cube = one grid cell of the 64³ simulation mesh. Best for seeing the grid structure and individual density values.
ψDM — Wave Dark Matter

Periodic interference fringes from superposition of plane waves.
ρ = |Σ Ai exp(i ki·r)|²

Khronon (τ framework)

Filamentary structure — nodes, filaments, voids.
Generated from multi-octave 3D noise mimicking cosmic-web topology.

CDM — Cold Dark Matter

Discrete point-like subhalos — random Gaussian blobs
scattered in space. ρ ∼ Σ M exp(−r²/2σ²)

What you are (and are not) seeing

What this visualization shows

  • Topology only — the spatial pattern (filamentary vs periodic vs discrete) of each dark matter model
  • Density fields are generated procedurally at 64³ resolution to illustrate the qualitative morphology
  • The Khronon pattern is based on our 2D simulation result: P(k) ~ k−2.2 broad continuum

What this does NOT show

  • Correct amplitude — real density perturbations are δρ/ρ ~ 1–10%, not the 100× contrast shown here
  • Visibility — dark matter does not emit, absorb, or scatter light in any wavelength. These structures are completely invisible
  • Correct scale — the predicted sub-structure lives within galaxy halos (~100 kpc), at sub-kpc scales. This is NOT the large-scale cosmic web

How would we actually detect this?

  • Gravitational lensing residuals — background light bent by the dark matter reveals ~1% brightness anomalies whose spatial statistics encode P(k)
  • Flux ratio anomalies in multiply-imaged quasars (e.g. HS 0810+2554)
  • Stellar stream gaps — dark perturbers create gaps in thin stellar streams (e.g. GD-1)
  • Distinguishing the three models requires measuring the power spectrum slope of lensing residuals across ~10 systems