Dark Matter, Dark Energy, and Open Questions

The preceding lessons reached the same two conclusions from different directions: most of the matter in the universe is not baryonic, and most of its present energy density is neither matter nor radiation. This closing lesson assembles the full evidence for dark matter, surveys the candidate particles and how experiments hunt them, states the six-parameter concordance model that fits everything, and sets out the problems the model does not solve. It is a summary of what the hot Big Bang has established and a map of where it stops.

The evidence chain for dark matter

No single observation proves dark matter; the case rests on the agreement of independent probes spanning galactic to cosmological scales, each measuring a mass that exceeds the visible baryons.

• Galaxy rotation curves. The orbital speed in spiral galaxies stays flat far beyond the visible disk, $v(r)\approx \text{const}$, requiring an enclosed mass $M(r)=v^{2}r/G$ that grows linearly with radius. The luminous matter cannot supply it; an extended dark halo can.
• Galaxy clusters. The velocity dispersion of cluster galaxies, applied to the virial theorem, and the temperature of the X-ray-emitting intracluster gas, both give cluster masses roughly ten times the baryonic mass. Zwicky's 1933 dynamical argument for the Coma cluster was the first such measurement.
• Gravitational lensing. The bending of background-galaxy light by foreground clusters measures the total gravitating mass independently of its dynamical state, and agrees with the virial and X-ray estimates. In the Bullet Cluster, two colliding clusters, the lensing mass is offset from the X-ray gas and tracks the collisionless galaxies, direct evidence that the dominant mass is collisionless and not the baryonic gas.
• The cosmic microwave background. The height of the third acoustic peak requires ${\Omega }_c{h}^2\approx 0.12$, several times the baryon density ${\Omega }_b{h}^2\approx 0.022$, measured entirely from the physics of the photon-baryon plasma at $z\approx 1090$.
• Structure formation. As shown in the previous lesson, the observed structure could not have grown from the $10^{-5}$ CMB perturbations without a non-baryonic, pressureless component whose growth begins before recombination.

The five probes measure different physics at different epochs and scales, and they agree on ${\Omega }_m\approx 0.31$ with ${\Omega }_b\approx 0.05$. The consistency is the argument.

Candidate particles and detection

Dark matter must be non-baryonic (from BBN and the CMB), cold or at most warm (to seed bottom-up structure), stable over the age of the universe, and weakly interacting (otherwise it would have been seen). Several candidates fit:

• WIMPs (weakly interacting massive particles). A stable particle with weak-scale mass ($\sim 100\text{GeV}$) and weak-scale cross section freezes out in the early universe with a relic abundance close to the observed ${\Omega }_c$ — the WIMP miracle. Supersymmetry supplies a natural candidate in the lightest neutralino.
• Axions. A very light pseudoscalar ($\sim 10^{-5}\text{eV}$) introduced to solve the strong-CP problem of quantum chromodynamics; produced non-thermally, it is cold despite its tiny mass.
• Sterile neutrinos. A right-handed neutrino ($\sim \text{keV}$) that mixes weakly with the active neutrinos; warm dark matter that could show up as an X-ray decay line.

The WIMP case is quantitative. A species in thermal equilibrium in the early universe stays coupled while its annihilation rate exceeds the expansion rate. Once $\Gamma =n⟨{\sigma }_{A}v⟩$ falls below $H$, the comoving number freezes at a relic abundance that scales inversely with the annihilation cross section,

A weak-scale cross section, $⟨{\sigma }_{A}v⟩\sim 10^{-26}{\text{cm}}^3{\text{s}}^{-1}$, yields ${\Omega }_{\text{dm}}{h}^2\approx 0.1$ — the observed value — without tuning. That a particle at the electroweak mass scale, motivated independently in particle physics, freezes out with precisely the required abundance is the WIMP miracle, and it is the reason weak-scale dark matter has been the leading hypothesis.

Three detection strategies follow from the same interaction vertex read in different directions:

• Direct detection watches for a dark-matter particle scattering off a nucleus in an underground detector, depositing keV of recoil energy. Experiments set increasingly stringent limits on the WIMP cross section.
• Indirect detection looks for the annihilation or decay products — gamma rays, positrons, neutrinos — from regions of high dark-matter density such as the Galactic center.
• Collider production seeks to create dark-matter particles in high-energy collisions, appearing as missing energy and momentum.

No candidate has been confirmed. Direct-detection limits have pushed deep into the WIMP parameter space without a signal, axion searches are scanning their mass range, and no collider excess has appeared. The particle nature of dark matter remains unknown.

The concordance model and its budget

The six-parameter $\Lambda$CDM model — the baryon density, cold-dark-matter density, Hubble constant (or the acoustic-scale parameter), scalar amplitude, scalar spectral index, and reionization optical depth — fits the CMB, the light-element abundances, the large-scale structure, the supernova Hubble diagram, and the baryon acoustic oscillation scale simultaneously. The present energy budget it implies is

with radiation negligible today. Dark energy dominates the present expansion, dark matter dominates the matter, and everything the periodic table describes is a twentieth of the total.

The independent probes not only agree on ${\Omega }_m$; they agree on the joint $({\Omega }_m,{\Omega }_{\Lambda })$ point. Supernova distances, CMB acoustic peaks, and baryon acoustic oscillations each carve out a band in the plane, and the three bands intersect at a flat, accelerating universe — the geometric statement of the concordance.

Open questions

The concordance model is empirically successful and theoretically incomplete. The open problems are not gaps in the fit but missing physics behind the parameters.

• The nature of dark energy. A cosmological constant with $w=-1$ fits, but its energy density is smaller than the natural vacuum-energy scale by some 120 orders of magnitude — the cosmological-constant problem. Whether dark energy is a true constant or a slowly evolving field (quintessence, $w\ne -1$) is unsettled; current data are consistent with $w=-1$ to about ten percent.

• The Hubble tension. The Hubble constant inferred from the CMB assuming $\Lambda$CDM, $H_0=67.4{\text{km s}}^{-1}{\text{Mpc}}^{-1}$, disagrees at the $4$–$5\sigma$ level with the local distance-ladder value near $73$. Either a systematic error remains undiagnosed, or the concordance model is missing an ingredient in the early universe.
• Small-scale structure. N-body simulations of cold dark matter predict more satellite galaxies and cuspier halo centers than some observations show (the missing-satellites and core-cusp problems). Whether these reflect baryonic physics in the simulations or a departure from cold, collisionless dark matter is debated.
• The matter-antimatter asymmetry. The universe contains baryons and essentially no antibaryons, an asymmetry $\eta \sim 10^{-9}$ that must have been generated in the early universe (baryogenesis). The Standard Model cannot produce it at the required level; new physics is needed.
• Before inflation. Inflation sets the initial conditions for the hot Big Bang but is itself a phenomenological framework; the identity of the inflaton, the physics of reheating, and whether spacetime had a beginning at all remain beyond the reach of current theory.

The hot Big Bang model quantitatively accounts for the expansion, the light elements from nucleosynthesis, the microwave background and its acoustic peaks, and the growth of structure from the perturbations that inflation supplies. The two components that dominate its energy budget, and the asymmetry that lets it contain matter at all, are named but not understood.¹