Dark Matter

Approximately 27% of the energy content of the universe consists of a mysterious substance that does not emit, absorb, or scatter light. We call it dark matter. Its existence is inferred entirely from its gravitational effects, and it is supported by evidence from scales ranging from individual galaxies to the entire observable universe. Despite decades of searching, its particle identity remains unknown, making dark matter one of the most profound open problems in physics.

Evidence for Dark Matter

Galaxy Rotation Curves

The most intuitive evidence comes from the rotation of spiral galaxies. For a star orbiting at radius $r$ from the galactic center, Newtonian mechanics gives:

$$v(r) = \sqrt{\frac{GM(r)}{r}}$$

where $M(r)$ is the mass enclosed within radius $r$. If most of the mass is concentrated in the luminous central region, we expect $v(r) \propto 1/\sqrt{r}$ at large radii (Keplerian decline). Instead, Vera Rubin and Kent Ford discovered in the 1970s that rotation curves remain flat out to large radii: $v(r) \approx \text{const}$.

This implies $M(r) \propto r$, meaning there is a large amount of unseen mass extending far beyond the visible disk. This mass is distributed in a roughly spherical dark matter halo surrounding each galaxy.

Gravitational Lensing

General relativity predicts that mass bends light. By measuring the distortion (shearing) of background galaxy images, we can map the total mass distribution in galaxy clusters. These weak lensing maps consistently show far more mass than is visible. Strong lensing: the dramatic arcs and multiple images seen around massive clusters, also requires dark matter to explain the observed deflection angles.

The Cosmic Microwave Background

As we saw in the previous lesson, the heights and positions of the acoustic peaks in the CMB power spectrum are sensitive to the baryon density $\Omega_b h^2$ and the total matter density $\Omega_m h^2$ independently. The CMB data show that $\Omega_m \approx 0.31$ while $\Omega_b \approx 0.05$: most of the matter is non-baryonic. This is entirely independent of any galaxy-scale measurement.

Structure Formation

Without dark matter, the tiny density perturbations seen in the CMB ($\delta\rho/\rho \sim 10^{-5}$) could not have grown into galaxies and clusters by today. Baryonic matter alone cannot form structures efficiently because photon pressure prevents gravitational collapse before recombination. Dark matter, which does not interact with photons, begins collapsing much earlier, creating the gravitational potential wells into which baryons later fall.

The Bullet Cluster

Perhaps the most direct evidence comes from the Bullet Cluster (1E 0657-558), where two galaxy clusters collided. X-ray observations show that the hot gas (which is the dominant baryonic component) was slowed by the collision, while weak lensing maps show that most of the mass passed right through, coinciding with the galaxies themselves. This is exactly what we expect if most of the mass is in a collisionless dark matter component. Modified gravity theories struggle to explain this spatial separation of mass from visible matter.

Properties of Dark Matter

Dark Matter Candidates

WIMPs (Weakly Interacting Massive Particles): Particles with masses of $\sim 10$-$1000$ GeV that interact via the weak force. Remarkably, the thermal relic abundance of a particle with weak-scale cross section naturally gives the observed dark matter density (the "WIMP miracle"): $\langle\sigma v\rangle \sim 3 \times 10^{-26} \text{ cm}^3/\text{s}$ yields $\Omega_\chi h^2 \approx 0.12$. Supersymmetric neutralinos are the canonical WIMP candidate.

Axions: Ultra-light bosons ($m \sim 10^{-5}$ eV) originally proposed to solve the strong CP problem in QCD. Despite their tiny mass, they are produced non-thermally (by the misalignment mechanism) and behave as cold dark matter. Axion dark matter would form a coherent oscillating field rather than individual particles.

Sterile neutrinos: Right-handed neutrinos with masses in the keV range. They mix weakly with active neutrinos and could be produced in the early universe. They would constitute "warm" dark matter, with observable consequences for small-scale structure.

Primordial black holes: Black holes formed in the early universe (not from stellar collapse) with masses potentially ranging from $10^{-15}$ to $10^{4}$ solar masses. Various observational constraints (microlensing, CMB distortions, gravitational wave limits) have ruled out most of the mass range, but some windows remain open.

Detection Methods

Direct detection: If dark matter particles occasionally scatter off ordinary nuclei, we can detect the resulting nuclear recoil in ultra-sensitive underground detectors. Experiments like LZ, XENONnT, and PandaX use tonnes of liquid xenon, shielded deep underground from cosmic rays. These experiments have achieved extraordinary sensitivity, ruling out WIMP-nucleon cross sections above $\sim 10^{-47}$ cm$^2$ for masses around 30 GeV. No confirmed detection has been made.

Indirect detection: If dark matter particles annihilate or decay, the products (gamma rays, neutrinos, positrons, antiprotons) may be detectable. Telescopes like Fermi-LAT, MAGIC, and IceCube search for these signals from regions of high dark matter density (galactic center, dwarf galaxies, galaxy clusters). Several tantalizing excesses have been reported but none conclusively confirmed as dark matter.

Collider production: If dark matter interacts with Standard Model particles, it could be produced at the LHC. Dark matter particles would escape the detector, appearing as "missing energy." Despite extensive searches, no evidence has been found, placing strong constraints on simplified dark matter models.

Modified Gravity: MOND

An alternative explanation, proposed by Mordehai Milgrom in 1983, modifies Newtonian dynamics (MOND) rather than invoking dark matter. MOND postulates that below a critical acceleration $a_0 \approx 1.2 \times 10^{-10}$ m/s$^2$, the gravitational force transitions from $F = ma$ to $F = m\sqrt{a \cdot a_0}$. Remarkably, MOND successfully predicts galaxy rotation curves with a single parameter.

However, MOND faces serious challenges: it cannot explain the Bullet Cluster, has difficulty matching the CMB power spectrum, and lacks a fully consistent relativistic formulation (though TeVeS and related theories have been proposed). Most cosmologists regard dark matter as far more successful as a comprehensive framework, though MOND's empirical successes on galaxy scales remain thought-provoking.

Key Insights

• Dark matter is supported by evidence from galaxy rotation curves, gravitational lensing, the CMB, structure formation, and the Bullet Cluster
• It must be massive, non-baryonic, cold, dark, collisionless, and stable
• Leading candidates include WIMPs, axions, sterile neutrinos, and primordial black holes
• Three complementary search strategies (direct, indirect, collider) have not yet yielded a detection
• The WIMP miracle provides a compelling theoretical motivation for weak-scale dark matter
• Modified gravity (MOND) can explain galaxy rotation curves but fails on cosmological scales
• Identifying dark matter would be one of the most important discoveries in the history of physics

Looking Ahead

Dark matter tells us that most of the matter in the universe is invisible. But there is an even more mysterious component: dark energy, which makes up 68% of the universe and is causing the expansion to accelerate. In the next lesson, we explore its discovery, its theoretical interpretation, and the profound puzzles it raises about the nature of the vacuum.