Missing Mass — scorecard

2026-05-24

I asked Anthropic’s Claude to produce this scorecard for my benefit in an aid for my studies. Maybe others might find it useful.

This is what it produced …


Competing theories of missing mass — scorecard

Status as of May 2026 · scored per observational domain · verdicts approximate

Score key: ✅ Strong · 🟢 Good · 🟡 Mixed · 🟠 Weak · ❌ Fails · — N/A


What problem are we solving?

Galaxies rotate too fast, clusters contain more mass than their visible matter accounts for, and the universe’s large-scale structure only makes sense if most of its matter is invisible. The theories below are the leading attempts to explain this. They fall into two broad camps: dark matter (there really is invisible matter) and modified gravity (our equations of gravity are wrong at low accelerations). Some entries — SIDM, fuzzy DM, primordial BHs — are variants within the dark matter camp rather than alternatives to it.


Galactic scale

Test / domain Λ-CDM MOND / MiHOG TeVeS / relativ. MOND SIDM Fuzzy DM Primordial BHs
Rotation curves (flat beyond the visible disc) 🟢 Good — halo profiles must be tuned per galaxy ✅ Strong — near-perfect fits with a single free parameter a 🟢 Good 🟢 Good 🟢 Good 🟡 Mixed — only viable if PBHs saturate halos
Radial Acceleration Relation (tight correlation between baryonic and total acceleration) 🟡 Mixed — trend reproduced statistically, not galaxy by galaxy ✅ Strong — predicted before measurement; direct consequence of a ✅ Strong 🟡 Mixed 🟡 Mixed 🟠 Weak
Tully–Fisher relation (MV⁴ for spirals) 🟢 Good — holds statistically across populations ✅ Strong — falls out analytically from MOND ✅ Strong 🟢 Good 🟢 Good 🟠 Weak
Dwarf spheroidal galaxies (velocity dispersions in low-surface-brightness dwarfs) 🟢 Good — DiRAC simulations reproduce observed kinematics 🟡 Mixed — struggles with isolated dwarfs in the external-gravity regime 🟡 Mixed 🟢 Good 🟢 Good

Note on MOND at galactic scales. MOND’s predictive success here is real and not fully accounted for by Λ-CDM without per-galaxy tuning. The Radial Acceleration Relation in particular was predicted by MOND before it was measured — a genuine scientific success.


Cluster scale

Test / domain Λ-CDM MOND TeVeS SIDM Fuzzy DM Primordial BHs
Galaxy cluster masses (lensing + X-ray gas fall short of total mass) ✅ Strong ❌ Fails — factor 2–3 mass deficit in every cluster studied (“cluster conundrum”) ❌ Fails — same deficit; sterile neutrinos are sometimes added as a patch 🟡 Mixed — cross-section requirements are scale-dependent and actively debated (see note) 🟢 Good 🟠 Weak
Bullet Cluster and merging clusters (mass centroid offset from gas; collisionless behaviour) ✅ Strong ❌ Fails — cannot separate gas from lensing peak without exotic baryons 🟠 Weak 🟡 Mixed — consistent with σ/m ≲ 0.22 cm²/g (2026 radio-relic constraint); harder to reconcile with dwarf-scale hints of larger cross-sections 🟢 Good 🟠 Weak

Note on SIDM cross-section tension. SIDM explains small-scale structure best with σ/m ~ 1–10 cm²/g, but cluster collisions and lensing now constrain σ/m ≲ 0.1–0.22 cm²/g at cluster velocities. Velocity-dependent cross-sections can bridge this gap, but the parameter space is narrowing. A March 2026 analysis of MACS J0138-2155 and an April 2026 double-radio-relic study (arXiv:2605.00093) provide the tightest recent cluster constraints.


Cosmological scale

Test / domain Λ-CDM MOND TeVeS SIDM Fuzzy DM Primordial BHs
CMB acoustic peaks (precise peak heights and positions) ✅ Strong — Λ-CDM’s single greatest success; the model was in large part fitted to CMB data ❌ Fails — no relativistic framework capable of reproducing peak structure 🟠 Weak — GW speed constraint (GW170817, 2017) ruled out original TeVeS; successor theories such as RMOND remain active 🟢 Good — follows CDM on large scales 🟢 Good 🟢 Good
Baryon Acoustic Oscillations (standard ruler in galaxy clustering) ✅ Strong ❌ Fails — no cosmological framework to predict the BAO scale 🟠 Weak ✅ Strong ✅ Strong 🟢 Good
Large-scale structure (matter power spectrum; cosmic web) ✅ Strong ❌ Fails — cannot generate the observed power spectrum 🟠 Weak ✅ Strong 🟡 Mixed — free-streaming suppresses small-scale power; the canonical ~10⁻²² eV mass is now in tension with Lyman-α data (see note) 🟢 Good
Kinetic Sunyaev–Zel’dovich effect ★ (peculiar velocities of ionised gas on Gpc scales) ✅ Strong — observed signal matches Λ-CDM predictions ❌ Fails — prediction significantly departs from observations ❌ Fails ✅ Strong 🟢 Good 🟢 Good

★ Result published April 2026.

Note on fuzzy DM mass constraints. The originally motivated mass range (~10⁻²² eV) is under serious pressure. Lyman-α forest observations now suggest m ≳ 2 × 10⁻²⁰ eV if fuzzy DM makes up all dark matter. This begins to undercut the small-scale motivation for the model. Lower mass fractions, or a combination with CDM, remain viable.


Small-scale tensions (challenges for Λ-CDM)

These three problems arise because Λ-CDM simulations, run without baryonic physics, predict more and denser structure on small scales than is observed. Baryonic feedback (supernovae, AGN) can partially resolve them, but the solutions require fine-tuning and are not yet fully satisfactory.

Test / domain Λ-CDM MOND TeVeS SIDM Fuzzy DM Primordial BHs
Core–cusp problem (simulations predict dense NFW cusps; observations show flat cores) 🟡 Mixed — baryonic feedback can produce cores but requires tuning 🟢 Good 🟢 Good ✅ Strong — self-interactions redistribute energy; core formation is a natural outcome ✅ Strong — a soliton core at the centre is a generic prediction
Missing satellites (Λ-CDM predicts far more sub-halos than observed satellite galaxies) 🟡 Mixed — reionisation and feedback suppress dwarf formation; not fully solved 🟢 Good — fewer substructures predicted naturally 🟢 Good 🟢 Good ✅ Strong — free-streaming cuts off small-scale power; note this is now in tension with the Lyman-α mass bound (see above)
Too-big-to-fail (the brightest predicted sub-halos are too dense to host observed satellites) 🟡 Mixed — baryonic solutions partially work 🟢 Good 🟢 Good 🟢 Good 🟢 Good

Direct and laboratory tests

Test / domain Λ-CDM MOND TeVeS SIDM Fuzzy DM Primordial BHs
Direct particle detection (underground WIMP detectors: XENONnT, PandaX-4T) 🟠 Weak — no detection after decades; now operating at the neutrino floor; WIMP parameter space shrinking fast — no particle to detect — self-interaction only; not lab-detectable in conventional sense 🟡 Mixed — axion searches (ADMX, HAYSTAC) ongoing; no detection yet 🟡 Mixed — GW merger rates and LHAASO γ-ray burst limits strongly constrain most mass windows (see note)
Gravitational wave speed (GW170817: c_gw = c to 10⁻¹⁵) ✅ Strong ❌ Fails — original TeVeS predicted c_gw ≠ c; effectively falsified as a standalone theory ✅ Strong ✅ Strong ✅ Strong

Note on primordial BH mass windows. Microlensing (OGLE, HSC), GW merger rates, CMB accretion constraints, and Hawking evaporation limits together close most of the mass range. The surviving windows are approximately 10¹⁷–10²³ g (asteroid-to-Moon mass), with ongoing debate about how much of this survives IGM heating and new cratering constraints (MNRAS, 2025). The stellar-mass window (~10–100 M☉) remains contentious; the LIGO/Virgo merger rate is consistent with a small PBH fraction but does not require it.


Overall standing

Theory Verdict Key strength Key weakness
Λ-CDM Leading paradigm Dominant on cosmic scales; CMB and BAO fits Small-scale tensions; no particle detected after decades of searching
MOND / MiHOG Galactic niche Predictive power on individual galaxy kinematics; RAR prediction Systematically fails at cluster and cosmological scales
TeVeS / relativistic MOND Largely ruled out Motivated relativistic extension of MOND GW speed measurement falsified original theory; successors (RMOND) still being developed
SIDM Viable Λ-CDM variant Naturally resolves core–cusp and related tensions Cross-section must be velocity-dependent to reconcile dwarf and cluster scales; parameter space tightening
Fuzzy dark matter Active but increasingly constrained Soliton cores; clean small-scale predictions Canonical ~10⁻²² eV mass window under pressure from Lyman-α; tension between small-scale motivation and cosmological constraints
Primordial black holes Heavily constrained No new physics required; testable with GW and lensing Most mass windows closed; only narrow asteroid-mass range viable for 100% DM fraction

SIDM, fuzzy dark matter, and primordial black holes are modifications within the dark matter paradigm, not alternatives to it. MOND’s predictive success on individual galaxy kinematics — particularly the Radial Acceleration Relation — is genuine and remains a challenge for Λ-CDM to explain without per-galaxy tuning. The core–cusp, missing satellites, and too-big-to-fail problems are real tensions for Λ-CDM, partially but not fully addressed by baryonic feedback in simulations. No single theory currently succeeds across all scales.