ΛCDM ✓ DM halos pass through Collisionless by assumption ✓ Gas gets stuck Electromagnetic interactions ✓ Lensing tracks DM halos Mass follows collisionless halos ✓ Cluster mass budget DM halos provide missing mass ~ Galaxy rotation curves Requires tuned halo profiles ✗ Identifies dark matter Unknown particle (not detected) ✗ Unifies galaxy + cluster No MOND explanation Works — but what IS the dark matter? Standard MOND ✗ No collisionless component Nothing to separate from gas ✓ Gas gets stuck Same as ΛCDM ~ Lensing offset direction Correct direction, wrong magnitude ✗ Cluster mass budget Factor ~2 residual deficit ✓ Galaxy rotation curves By construction (a₀ fitted) — Identifies dark matter Not applicable (no DM) ✗ Unifies galaxy + cluster MOND fails at cluster scales Directionally right, quantitatively wrong Substrate ✓ Substrate passes through Normal phase: collisionless ✓ Gas gets stuck Same as ΛCDM ✓ Lensing tracks substrate Substrate = DM in normal phase ✓ Cluster mass budget n₁m₁ = ρ_DM (C10) ✓ Galaxy rotation curves Superfluid phase → MOND ✓ Identifies dark matter dc1 substrate itself ✓ Unifies galaxy + cluster One phase transition (v_L) Predicted — phase transition resolves MOND's cluster problem Key distinction: the substrate is the same substance in both phases — superfluid (MOND) in galaxies, incoherent (CDM) in clusters. The transition is at vL ≈ 750 km/s, from galactic dynamics — not fitted to clusters. ✓ Successful ~ Partial ✗ Fails — Not applicable
Figure: Three-framework comparison for the Bullet Cluster. ΛCDM explains the lensing-gas offset but cannot identify the dark matter particle. Standard MOND gets the offset direction right but has a factor ~2 mass deficit and no collisionless component. The substrate framework resolves both: the dc1 medium is collisionless in its normal (incoherent) phase at cluster velocity dispersions, providing the correct mass budget while the same substance produces MOND phenomenology in galaxies through its superfluid phase.