The case for dark matter rests on multiple independent lines of evidence, all pointing to the same conclusion: the gravitational dynamics of the universe require far more mass than we can see. What makes the case compelling is not any single observation, but the convergence of evidence across vastly different scales and physical phenomena.
Galaxy Rotation Curves
The most historically significant evidence comes from the rotation curves of spiral galaxies. For a star orbiting at radius \(r\) from a galaxy’s centre, circular motion requires
\[ v(r) = \sqrt{\frac{G M(r)}{r}} \]
where \(M(r)\) is the mass enclosed within radius \(r\). Beyond the visible disc, where luminous matter becomes sparse, we’d expect \(M(r) \approx \text{const}\) and hence \(v \propto r^{-1/2}\)—a Keplerian decline.
Vera Rubin and Kent Ford’s observations in the 1970s showed something quite different: rotation curves remain approximately flat out to large radii. This implies \(M(r) \propto r\), meaning substantial mass exists well beyond the visible galaxy. The required mass distribution is consistent with a roughly spherical “halo” with density profile \(\rho(r) \propto r^{-2}\) in the outer regions.
Galaxy Cluster Dynamics
Fritz Zwicky first noticed the problem in the 1930s studying the Coma Cluster. Applying the virial theorem to a gravitationally bound system in equilibrium:
\[ 2\langle K \rangle + \langle U \rangle = 0 \]
From measured velocity dispersions \(\sigma_v\), the total kinetic energy gives an estimate of the gravitational potential energy required to bind the cluster, and hence its total mass. Zwicky found the dynamical mass exceeded the luminous mass by a factor of order 100. He called the missing component “dunkle Materie.”
Modern measurements using galaxy velocities in clusters consistently show mass-to-light ratios of \(M/L \sim 200\)–\(300 \, M_\odot / L_\odot\), far exceeding that of stellar populations.
Gravitational Lensing
General relativity predicts that mass curves spacetime, bending light paths. The deflection angle for a light ray passing a mass \(M\) at impact parameter \(b\) is
\[ \alpha = \frac{4GM}{c^2 b} \]
This provides a mass measurement independent of dynamical assumptions.
Strong lensing produces multiple images or arcs when a massive cluster lies along the line of sight to a background galaxy. Reconstructing the lens mass distribution consistently reveals far more mass than the visible galaxies and hot gas contain.
Weak lensing measures subtle statistical distortions of background galaxy shapes, mapping the total mass distribution across large areas of sky. These maps show mass concentrations tracing the large-scale structure, with total mass far exceeding baryonic content.
The Bullet Cluster
The Bullet Cluster (1E 0657-56) provides perhaps the most direct evidence. Two galaxy clusters have passed through each other, and we can separately map three components:
- Galaxies (visible light): passed through with little interaction
- Hot gas (X-ray emission): the dominant baryonic mass, slowed by ram pressure and lies between the clusters
- Total mass (weak lensing): concentrated around the galaxies, not the gas
The lensing mass is spatially offset from the baryonic mass. This is very difficult to explain with modified gravity theories, which tie gravitational effects to baryonic matter. Dark matter, being collisionless, would pass through like the galaxies, matching the observations.
Cosmic Microwave Background
The CMB power spectrum encodes information about the early universe’s composition. Before recombination, baryons were coupled to photons, and this fluid underwent acoustic oscillations in gravitational potential wells. The pattern of peaks in the angular power spectrum depends sensitively on cosmological parameters.
Baryons contribute inertia to the oscillations, while dark matter provides gravitational potential wells without contributing to the pressure. The relative heights of odd and even peaks (compression vs rarefaction) constrain the baryon-to-photon ratio \(\eta_b\) and the total matter density \(\Omega_m\) independently.
The Planck satellite measurements give:
\[ \Omega_b h^2 = 0.0224 \pm 0.0001 \] \[ \Omega_c h^2 = 0.120 \pm 0.001 \]
where \(\Omega_b\) is the baryon density, \(\Omega_c\) is the cold dark matter density, and \(h \approx 0.67\) is the reduced Hubble constant. Dark matter outweighs baryonic matter roughly 5:1.
Big Bang Nucleosynthesis
The abundances of light elements (D, \({}^3\text{He}\), \({}^4\text{He}\), \({}^7\text{Li}\)) synthesised in the first few minutes depend sensitively on the baryon-to-photon ratio. The observed primordial abundances constrain
\[ \Omega_b h^2 \approx 0.022 \]
in remarkable agreement with the CMB. Crucially, this is far below the total matter density required by dynamics and structure formation. The excess cannot be baryonic—it would spoil nucleosynthesis predictions.
Large-Scale Structure Formation
Galaxies and clusters are not distributed uniformly but form a cosmic web of filaments, walls, and voids. This structure grew from tiny primordial density perturbations via gravitational instability.
Baryonic matter alone cannot form structure quickly enough. Before recombination, baryons were coupled to radiation and couldn’t collapse. After recombination, the time available is insufficient to grow the observed structures from the small initial perturbations (\(\delta \rho / \rho \sim 10^{-5}\)) seen in the CMB.
Dark matter, being non-interacting, decoupled early and began collapsing sooner, creating potential wells into which baryons later fell. N-body simulations with cold dark matter reproduce the observed cosmic web remarkably well.
What Dark Matter Is Not
The evidence constrains what dark matter can be:
- Not hot gas: X-ray observations account for intracluster gas, and it’s insufficient
- Not stellar remnants or brown dwarfs (MACHOs): microlensing surveys rule out most of the mass range
- Not neutrinos: they’re too light and fast (“hot” dark matter), washing out small-scale structure
- Not a modification of gravity: the Bullet Cluster separation of mass from baryons, plus the detailed CMB/structure formation fits, strongly disfavour this
Current Picture
The concordance \(\Lambda\)CDM cosmology fits all these observations with roughly 27% matter (of which about 5% baryonic, 22% cold dark matter) and 73% dark energy. The leading particle candidates are weakly interacting massive particles (WIMPs) and axions, though direct detection experiments have yet to find a signal.
The remarkable feature is the consistency: rotation curves, cluster dynamics, lensing, the CMB, nucleosynthesis, and structure formation all independently point to the same dark matter density. This convergence is what makes the case so strong, even without knowing what dark matter actually is.