Dark Matter Theories to Know

Why This Matters

Dark matter makes up roughly 27% of the universe's total mass-energy content, yet it has never been directly detected. You're being tested on your understanding of why we think dark matter exists (gravitational evidence like galaxy rotation curves and gravitational lensing) and how different theoretical frameworks attempt to explain it. The theories here represent fundamentally different approaches: particle physics candidates, modifications to gravity itself, and exotic cosmological objects.

Don't just memorize names and definitions. Know what problem each theory solves and where it struggles. Exam questions often ask you to compare approaches or evaluate which theory best explains a specific observation. Understanding the underlying physics will help you tackle both multiple choice and FRQ prompts.

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Particle Dark Matter Candidates

Most mainstream dark matter research focuses on undiscovered particles that interact gravitationally but barely (if at all) through other forces. The key distinction among particle candidates is their mass and velocity, which determines how they clump and influence structure formation.

Cold Dark Matter (CDM)

CDM particles are slow-moving and massive, so they clump efficiently under gravity. This property makes CDM the foundation of the standard cosmological model ($\Lambda$CDM).

• Dark matter halos form around galaxies, extending far beyond visible matter and explaining flat rotation curves where $v(r) \approx \text{constant}$ at large radii
• Large-scale structure predictions from CDM simulations match observations of galaxy clusters and cosmic web filaments remarkably well, making CDM the benchmark against which all other theories are measured

Weakly Interacting Massive Particles (WIMPs)

WIMPs are the most studied CDM candidate. They are hypothetical particles with masses in the range $\sim 10\text{–}1000 \text{ GeV}$ that interact only via gravity and the weak nuclear force.

• Thermal relic abundance: In the early universe, WIMPs were in thermal equilibrium with other particles. As the universe expanded and cooled, they "froze out" at a density that naturally matches the observed dark matter abundance. This coincidence is called the WIMP miracle and is a major reason WIMPs attracted so much theoretical attention.
• Direct detection experiments (LUX, XENON, LZ) search for rare WIMP-nucleus collisions by watching for tiny nuclear recoils in ultra-pure detector materials. No confirmed detection has been made, and exclusion limits are tightening the viable parameter space considerably.

Axions

Axions are ultra-light particles ($m \sim 10^{-5} \text{ eV}$) originally proposed to solve the strong CP problem in quantum chromodynamics, which is the puzzle of why the strong force doesn't violate CP symmetry even though QCD allows it.

• Produced non-thermally in the early universe, axions can form a cold, coherent field rather than behaving as individual particles. Despite their tiny mass, they act as cold dark matter because they were never in thermal equilibrium.
• Detection relies on photon conversion: in a strong magnetic field, an axion can convert into a photon (and vice versa). The ADMX experiment uses a tunable microwave cavity inside a powerful magnet to search for this signal.

Sterile Neutrinos

Sterile neutrinos are right-handed neutrinos that don't participate in the standard weak interaction. With masses in the $\text{keV}$ range, they sit between the ultra-light axion and the heavy WIMP, making them warm dark matter candidates.

• Produced through oscillation with active (standard model) neutrinos in the early universe. Their abundance depends sensitively on the mixing angle between sterile and active flavors.
• X-ray signatures could reveal their radiative decay (a sterile neutrino decaying into an active neutrino plus a photon). The unexplained 3.5 keV emission line observed in some galaxy clusters sparked significant interest, though its interpretation remains controversial and may have instrumental explanations.

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Alternative Particle Frameworks

Some theories modify how dark matter particles behave or introduce new physics beyond the simplest cold, collisionless model. These are motivated by specific observational tensions at small scales.

Self-Interacting Dark Matter (SIDM)

Standard CDM assumes dark matter particles are collisionless, passing through each other like ghosts. SIDM relaxes this assumption: dark matter particles scatter off each other with a cross-section of order $\sigma/m \sim 1 \text{ cm}^2/\text{g}$.

• Solves the core-cusp problem: CDM simulations predict steep density "cusps" at the centers of dark matter halos, but observations of dwarf galaxies often show flat density "cores." SIDM interactions redistribute kinetic energy among particles, thermalizing the inner halo and naturally producing cores.
• Preserves large-scale success of CDM because the interaction rate is too low to matter on cluster and cosmological scales, where CDM already works well.

Warm Dark Matter

Warm dark matter consists of intermediate-velocity particles with masses in the $\sim \text{keV}$ range. They move faster than CDM particles but slower than relativistic "hot" dark matter (like standard neutrinos).

• Free-streaming erases small structures: because these particles travel significant distances before slowing down enough to clump, density perturbations below a characteristic scale get washed out. This suppresses the formation of the smallest halos.
• Reduces the satellite galaxy overabundance: CDM predicts far more dwarf satellite galaxies around hosts like the Milky Way than are actually observed. Warm dark matter naturally produces fewer small halos, easing this tension.

Fuzzy Dark Matter

Fuzzy dark matter proposes ultra-light bosons with masses around $m \sim 10^{-22} \text{ eV}$. At these masses, the de Broglie wavelength reaches galactic scales ($\sim \text{kpc}$), so the dark matter behaves as a quantum wave rather than as discrete particles.

• Suppresses small-scale structure through quantum pressure (the uncertainty principle prevents confinement below the de Broglie wavelength), addressing the same CDM tensions as warm dark matter but through entirely different physics.
• Solitonic cores form at halo centers: stable, standing-wave interference patterns that produce flat density profiles, potentially matching observed cores in dwarf galaxies.

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Non-Particle Approaches

Not all dark matter theories invoke new particles. Some modify gravity itself, and others propose that dark matter consists of macroscopic objects made from known physics.

Modified Newtonian Dynamics (MOND)

MOND takes a radically different approach: instead of adding invisible matter, it alters Newton's second law at very low accelerations. Below a critical threshold $a_0 \approx 1.2 \times 10^{-10} \text{ m/s}^2$, the effective gravitational acceleration transitions from the Newtonian $a = GM/r^2$ to $a = \sqrt{GMa_0}/r$, which naturally produces flat rotation curves.

• Successfully predicts rotation curves of individual galaxies using only the distribution of visible matter. The baryonic Tully-Fisher relation (luminosity scaling as $v_{\text{flat}}^4$) emerges naturally from MOND rather than needing to be imposed.
• Struggles with galaxy clusters and cosmology: MOND cannot fully account for the mass discrepancy in galaxy clusters (it still needs some unseen mass), and it does not reproduce the CMB power spectrum or large-scale structure without significant additions. The Bullet Cluster, where the gravitational lensing signal is offset from the visible baryonic gas, is particularly difficult for pure MOND to explain.

Primordial Black Holes

These are black holes formed in the early universe from extreme density fluctuations during or shortly after inflation, not from stellar collapse. Their masses could span an enormous range, from $10^{-18} M_\odot$ to thousands of $M_\odot$.

• Gravitational detection is the primary search strategy: microlensing surveys (like EROS, OGLE, and Subaru/HSC) look for temporary brightening of background stars, and gravitational wave observatories (LIGO/Virgo) can detect mergers.
• Constrained but not ruled out: microlensing, CMB spectral distortions, and dynamical arguments have excluded most mass ranges. However, the asteroid-mass window ($\sim 10^{17}\text{–}10^{23} \text{ g}$) remains viable because these objects are too light to produce detectable microlensing and too heavy to have evaporated via Hawking radiation.

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Exotic and Speculative Models

These theories push beyond mainstream approaches, proposing entirely new sectors of physics.

Mirror Dark Matter

Mirror dark matter posits a parallel "mirror sector" of particles that duplicates the Standard Model: mirror protons, mirror electrons, mirror photons, all interacting among themselves via mirror forces.

• Explains dark matter's invisibility: mirror particles interact gravitationally with ordinary matter but have their own separate electromagnetic and nuclear forces, so they neither emit nor absorb our photons.
• Could address the matter-antimatter asymmetry if the mirror sector evolved with a different baryon asymmetry, potentially providing linked insights into baryogenesis in both sectors.

This model is highly speculative and difficult to test, but it illustrates how dark matter could be just as complex as visible matter while remaining completely hidden from our detectors.

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Quick Reference Table

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Self-Check Questions

1. Which two particle candidates are both produced in the early universe but differ dramatically in mass (one at $\text{GeV}$ scales, one at $10^{-5} \text{ eV}$)? What detection methods apply to each?

2. Compare and contrast how Warm Dark Matter and Fuzzy Dark Matter each address the small-scale structure problems of standard CDM. What's the key physical mechanism in each case?

3. A galaxy's rotation curve is flat at large radii. Which theories could explain this observation, and which would invoke new particles versus modified physics?

4. Why does MOND successfully predict individual galaxy rotation curves but struggle with galaxy cluster observations? What does this suggest about the theory's limitations?

5. If primordial black holes in the asteroid-mass range ($10^{17}\text{–}10^{23} \text{ g}$) constitute dark matter, how might we detect them, and why have other mass ranges been constrained?