34.4 Dark Matter and Closure

Dark Matter

Dark matter is an invisible form of matter that doesn't emit, absorb, or reflect light, yet it makes up roughly 27% of the total energy content of the universe. Understanding dark matter is central to explaining why galaxies hold together, how large-scale structures formed, and what the ultimate fate of the universe might be.

Evidence for Dark Matter

Several independent lines of evidence point to large amounts of unseen mass throughout the universe.

• Galactic rotation curves show that stars at the outer edges of galaxies orbit much faster than predicted by the visible mass alone. If only luminous matter were present, orbital speeds should drop off with distance from the center. Instead, they stay roughly flat, suggesting a halo of unseen mass extends well beyond the visible galaxy. The Milky Way's own rotation curve shows this pattern.
• Gravitational lensing occurs when a massive foreground object bends light from a more distant source. The amount of bending observed around galaxy clusters is far greater than visible matter can explain. The Bullet Cluster is a striking example: two colliding galaxy clusters where the gravitational lensing map (tracing total mass) is offset from the hot gas (tracing ordinary matter), directly revealing the presence of dark matter.
• Velocity dispersion in galaxy clusters refers to the spread of velocities among galaxies within a cluster. In the Coma Cluster, galaxies move so fast that the visible mass alone couldn't gravitationally bind them. Fritz Zwicky first noticed this discrepancy in the 1930s, providing some of the earliest evidence for dark matter.
• Cosmic microwave background (CMB) anisotropies are tiny temperature fluctuations in the afterglow of the Big Bang. Missions like WMAP and the Planck satellite measured these fluctuations in detail. The pattern of peaks in the CMB power spectrum is consistent with a universe containing about five times more dark matter than ordinary matter.
• Mass-to-light ratios of galaxies and galaxy clusters are much higher than expected from visible matter alone. This means there's far more gravitational mass present than the light output can account for.

Neutrino Oscillations and Dark Matter

Neutrinos come in three flavors: electron, muon, and tau. Neutrino oscillations are the phenomenon where neutrinos switch between these flavors as they travel. This was first confirmed through observations of solar neutrinos (which arrived at Earth in fewer numbers than expected) and atmospheric neutrinos.

The key physics point: oscillations can only happen if neutrinos have non-zero mass. This means neutrinos do contribute some mass to the universe. However, their individual masses are extremely small (upper bounds are fractions of an eV), so they can't account for all the dark matter.

Neutrinos are classified as "hot" dark matter because they move at relativistic (near-light) speeds. Simulations show that hot dark matter alone would smooth out the small-scale clumping needed to form galaxies and galaxy clusters. The observed large-scale structure of the universe matches much better with "cold" dark matter, which moves at non-relativistic speeds and can clump effectively on smaller scales.

Dark Matter Candidates: MACHOs vs. WIMPs

Dark matter candidates fall into two broad categories: baryonic (made of ordinary protons and neutrons) and non-baryonic (made of some new type of particle). Current evidence strongly favors non-baryonic matter as the dominant component.

MACHOs (Massive Compact Halo Objects) are baryonic candidates. These include objects like black holes, neutron stars, and brown dwarfs that emit little or no light, making them hard to detect directly. Surveys like the MACHO project and the EROS survey searched for MACHOs using gravitational microlensing, where a compact object passing in front of a distant star causes a temporary brightening. These surveys found some microlensing events, but not nearly enough to explain all the dark matter. MACHOs can account for only a small fraction of the total.

WIMPs (Weakly Interacting Massive Particles) are non-baryonic candidates. These are hypothetical particles that interact only through gravity and the weak nuclear force, making them extremely difficult to detect. Theoretical examples include neutralinos (predicted by supersymmetry) and Kaluza-Klein particles (predicted by extra-dimensional theories). WIMPs are classified as cold dark matter because their relatively large mass means they move at non-relativistic speeds.

WIMPs are currently the favored explanation because:

• They are "cold," matching the observed large-scale structure of the universe
• They naturally produce roughly the right abundance in the early universe (sometimes called the "WIMP miracle")
• Big Bang nucleosynthesis limits how much of the universe's matter can be baryonic, ruling out MACHOs as the primary component

Cosmological Implications

The density of the universe determines its overall geometry and long-term fate. Critical density is the specific average density of matter and energy needed for the universe to be geometrically flat (neither positively nor negatively curved). If the total density equals the critical density, the universe is flat.

Current observations (especially from the CMB) indicate the universe is very close to flat. The total energy budget breaks down roughly as:

• ~5% ordinary (baryonic) matter
• ~27% dark matter
• ~68% dark energy

Dark energy, often represented by the cosmological constant ($\Lambda$) in Einstein's field equations, drives the accelerating expansion of the universe. Together, dark matter and dark energy determine the geometry and ultimate fate of the cosmos. With dark energy dominating, the universe appears headed toward continued accelerating expansion rather than a collapse.