DM · Cosmology · Five questions to investigate
What is the gravitating component that light does not reveal?
Which properties of the unseen component are required by independent observations, and which production or interaction mechanisms can satisfy them together?
Starting knowledge: Newtonian gravity, particle collisions, and thermal equilibrium. Cosmological expansion is introduced where needed.
Visible stars and gas do not, under ordinary gravity, account for all observed gravitational effects. Galaxy rotation measures the acceleration needed for orbital motion. Gravitational lensing measures how spacetime bends light. The microwave background measures the evolution of an early plasma coupled to gravity. These are different probes, with different assumptions. Their combined interpretation in standard cosmology requires a substantial component that does not participate in ordinary electromagnetic plasma dynamics. [10]
“Dark” describes weak electromagnetic visibility, not a known species. The component might be particles produced in a hot plasma, a very light coherent field, or a population of compact objects in allowed ranges. An altered gravitational law is a competing explanatory strategy. It must address the same collection of observations, including growth of structure and lensing, rather than only one successful galaxy fit.
Cluster mergers provide a particularly instructive comparison. Hot gas collides and slows, while galaxies pass more freely. In the Bullet Cluster, lensing peaks are displaced from the dominant visible gas component. This strongly supports an additional, relatively collisionless gravitating component in the standard interpretation. Treating it as identification of a particle or a theorem excluding every possible modified-gravity theory would go beyond the measurement. [11]
Dated update, 1 September 2026. LZ reported one unusual event in an extended nuclear-recoil search, with global tension of $2.6$ standard deviations against its background-only model. The larger local significance does not account for all tested possibilities. The result is an interesting anomaly, not a confirmed dark-matter detection. It concerns a particular analysis and class of interactions. [12]
The particle mass, nongravitational interactions, and production history remain unestablished. A null search excludes a region of a specified model; it cannot exclude every dark component. Likewise, a relic-density calculation yielding the observed abundance does not establish that its particle exists.
For a spherical mass distribution in Newtonian gravity, a circular orbit at radius $r$ obeys
Here $v_c$ is circular speed and $M(<r)$ the enclosed mass. If the speed stays approximately constant at large $r$, the inferred mass increases approximately as $r$. Differentiating gives
This reconstructs an effective halo density only under the stated assumptions. Real disks are not spherical, stellar mass estimates are uncertain, and gas motion need not be exactly circular. The value of the exercise is that it separates the measured kinematics from the inference of mass and then from its proposed composition.
Suppose a stable particle $\chi$ once equilibrated with the thermal plasma. For definiteness, take a self-conjugate species, meaning that it is its own antiparticle, and let $n_\chi$ count individual particles. Pair annihilation removes particles; inverse collisions recreate them. In a homogeneous expanding universe,
The density is $n_\chi$, its equilibrium value is $n_{\rm eq}$, and $\langle\sigma v\rangle$ is the thermally averaged annihilation cross section times relative speed. The term $3Hn_\chi$ is dilution by expansion. The equation assumes a suitable kinetic distribution and the specified annihilation convention.
When $n_{\rm eq}\langle\sigma v\rangle$ greatly exceeds $H$, reactions approximately maintain equilibrium. Once annihilation cannot keep up, the abundance departs from its exponentially falling equilibrium value. It does not instantly stop evolving: residual annihilations continue. Under entropy-conserving expansion, $Y=n_\chi/s$ factors out dilution, with $s$ the plasma entropy density.
After departure from equilibrium, and under radiation domination with approximately constant relativistic degrees of freedom, set $x=m_\chi/T$ and collect constants into a positive dimensionless $\lambda$. For approximately constant $\langle\sigma v\rangle$,
Here $x_f$ is a starting point where the equilibrium term is already negligible, not a universally fixed temperature. Larger annihilation strength generally leaves fewer survivors.
Freeze-in works differently: a feebly coupled species never equilibrates, and rare production gradually builds its abundance. Increasing a sufficiently small production coupling can increase the final abundance. This reversed trend is a useful discriminant between mechanisms. The detailed temperature sensitivity depends on the interaction; not all freeze-in models are insensitive to the highest temperature. [13]
Calibration questions have established answers. Diagnostics ask what follows inside a specified model or comparison. Extensions are bounded proposals whose novelty and feasibility need a focused literature check. Each answer should record its assumptions and limits.
Do: Derive the density above and compare with a centrally concentrated luminous mass whose large-radius speed falls as $r^{-1/2}$.
Check: Keep units explicit and identify the spherical and equilibrium assumptions. A halo extending to infinity has infinite mass, so introduce a finite outer range.
Meaning: Clarifies the difference between a robust kinematic discrepancy and a unique microscopic interpretation.
Do: Integrate the abundance equation using an explicit equilibrium density and compare with the post-freeze-out solution above. Vary the annihilation strength.
Check: Test the early equilibrium and late constant-yield limits; tighten numerical tolerances near departure from equilibrium.
Meaning: Produces a relic-abundance mechanism you can explain quantitatively. It assumes the thermal and expansion history.
Do: Tune one freeze-out and one simple decay-driven freeze-in model to the same final density. Compare the momentum distribution and a scattering observable.
Check: Verify that the freeze-in species never equilibrates and that both parameter choices satisfy their approximations.
Meaning: Shows why matching abundance is insufficient and identifies information needed to break the degeneracy.
Do: Derive the maximum elastic recoil energy $E_R^{\max}=2\mu_{\chi N}^2v^2/m_N$, with reduced mass $\mu_{\chi N}$ and nuclear mass $m_N$. Compare light and heavy particles.
Check: Fold a specified speed distribution, threshold, and efficiency into a rate before interpreting an event count.
Meaning: Separates particle physics, halo assumptions, and detector sensitivity. A high-energy event need not be compatible with every familiar dark-matter model.
Do: Choose two nuclear targets and one interaction. Ask whether a cross-target rate ratio or common minimum-speed interval reduces sensitivity to the unknown speed distribution.
Check: Include nuclear response and threshold differences. Reproduce one existing halo-independent construction before modifying it.
Meaning: A bounded inference problem with established predecessors; a failure to remove the degeneracy is still an informative result.
Begin with DM-1 and DM-2. The first explains why an extra component is inferred; the second explains how a candidate could acquire its abundance. Keep those arguments separate until a model connects both and yields an independently testable consequence.
Vacuum energy and cosmic acceleration · Strong CP and the axion · Neutrino mass and identity · The origin of cosmic structure