The Dark Sector: Evidence Without Explanation

Rotation curves, gravitational lensing, cluster dynamics, the microwave-background budget and the supernova acceleration all say the same thing: gravitating matter exceeds luminous matter by about a factor of five, and the expansion of the universe is speeding up. This chapter records what is actually measured, and states honestly that no laboratory detection of a dark-matter particle exists and no mechanism for the acceleration has been identified. It is the largest quantitative discrepancy in physics between a well-tested theory — general relativity plus the Standard Model — and observation, and it is the reason the treatise has a Frontiers part at all.

The chapter is organized observation-first, on purpose. Candidate theories are named only where a search has been carried out and returned a null result or a bound, so that the reader can see which statements rest on data and which rest on nothing. It depends on the cosmological model of Evidence-Based Cosmology, the microwave-background measurements of Experiment: The Cosmic Microwave Background and the lensing formalism of The Einstein Field Equations; its particle-physics side draws on Cosmic Rays and Astroparticle Physics and on the neutrino limits of Experiment: Neutrino Oscillations. What remains unresolved is carried forward to What We Observe but Do Not Understand; the closely related question of whether gravity itself needs modifying at the quantum level is separate and belongs to Quantum Gravity: The Honest Status. A standard review of the particle side is [Bertone:2005].

The dynamical evidence

Cluster velocity dispersions

[Reserved: Zwicky's application of the virial theorem to the Coma cluster, finding a velocity dispersion far larger than the luminous mass supports and coining dunkle Materie [Zwicky:1933]; the more careful English restatement four years later, with the mass-to-light ratio and its assumptions made explicit [Zwicky:1937]; the virial theorem itself from Central Forces and Statics; why a factor of order a hundred in mass-to-light ratio was disbelieved for four decades, and what later reduced it to a factor of a few hundred in solar units.]

Galaxy rotation curves

[Reserved: Rubin and Ford's spectroscopic rotation curve of Andromeda, flat far beyond the optical disc [Rubin:1970]; the survey of twenty-one spirals that made the result general and unavoidable [Rubin:1980]; the Keplerian expectation \(v\propto r^{-1/2}\) against the observed \(v\approx\text{const}\), and the implied enclosed mass \(M(r)\propto r\); the mass discrepancy as a function of radius rather than a single global number.]

Neutral-hydrogen curves beyond the optical disc

[Reserved: the \(21\,\mathrm{cm}\) hyperfine line as a kinematic tracer where there are no stars; Bosma's radio survey extending rotation curves to several optical radii [Bosma:1981]; the detailed mass decomposition of NGC 3198 into disc and halo, which showed that no plausible disc mass-to-light ratio removes the need for a halo [vanAlbada:1985]; the maximum-disc degeneracy and what breaks it.]

Galaxy stability and halo masses

[Reserved: the argument of Ostriker, Peebles and Yahil that cold self-gravitating discs are unstable to bar formation unless embedded in a massive halo, and their compilation of dynamical masses growing with the radius sampled [Ostriker:1974]; satellite kinematics and the timing argument for the Local Group; why an independent line of reasoning arriving at the same halo was what turned the discrepancy from an anomaly into a research programme.]

X-ray hydrostatic cluster masses

[Reserved: the hot intracluster medium in hydrostatic equilibrium, whose temperature and density profiles from Chandra give a total mass profile independent of galaxy kinematics [Vikhlinin:2006]; the resulting gas fraction of about \(12\,\mathrm{\%}\), consistent with the cosmological baryon fraction and inconsistent with the cluster being made of what it is made of; the baryon budget compared against Section 134.3.2.]

Gravitational lensing

Strong lensing

[Reserved: Einstein's short note on the lens-like action of a star [Einstein:1936], with the deflection angle from The Einstein Field Equations; the discovery of the twin quasar 0957+561 as the first observed gravitational lens [Walsh:1979]; Einstein rings and giant arcs in clusters; lensing masses as a purely geometric probe requiring no assumption of dynamical equilibrium, which is why they matter here.]

Weak lensing and shear surveys

[Reserved: the first detection of coherent image alignments behind clusters [Tyson:1990]; the statistical measurement of cosmic shear over wide fields, mapping the projected mass distribution directly; modern survey constraints from the Dark Energy Survey [Abbott:2022] and from KiDS [Asgari:2021]; the shear two-point function and the parameter combination \(S_{8}=\sigma_{8}\sqrt{\Omega_{m}/0.3}\) it measures, whose mild disagreement with the microwave background is taken up in Section 134.7.2.]

The Bullet Cluster

[Reserved: the merging cluster 1E 0657-56, in which the X-ray emitting gas — most of the baryonic mass — is displaced from the lensing mass peaks that track the galaxies [Clowe:2006]; why this is the single cleanest argument that the missing mass is not a failure of the gravitational force law, since here the mass and the baryons are spatially separated; the accompanying bound on the dark-matter self-interaction cross-section per unit mass, of order \(0.1\,\mathrm{m}^{2}/\mathrm{kg}\) [Markevitch:2004], which constrains self-interacting candidates.]

Microlensing and the compact-object bound

[Reserved: Paczyński's proposal to detect massive compact halo objects by the transient magnification of background stars [Paczynski:1986]; the EROS-2 survey of the Magellanic Clouds, which excluded such objects as the dominant halo component over roughly \(10^{-7}\) to \(10\) solar masses [Tisserand:2007]; the conclusion that the missing mass is not ordinary matter in dark lumps, which together with Section 134.3.2 closes off the astrophysically conservative options.]

Cosmological evidence

The microwave-background budget

[Reserved: the acoustic peak structure of the temperature and polarization power spectra, and the separate roles of baryons and of pressureless dark matter in setting the peak heights — \(\Omega_{b}h^{2}=0.0224\) against \(\Omega_{c}h^{2}=0.120\), a factor above five [Aghanim:2020]; the measurement itself in Experiment: The Cosmic Microwave Background; why a component that does not couple to photons is required by the ratio of odd to even peaks, not merely allowed by it.]

Nucleosynthesis and the baryon count

[Reserved: primordial abundances of deuterium, helium-3, helium-4 and lithium-7 as a one-parameter function of the baryon-to-photon ratio, and the resulting independent baryon density [Cyburt:2016]; its agreement with the microwave-background value to a few percent, which is a genuine concordance across an epoch ratio of about \(10^{5}\); the lithium-7 discrepancy stated honestly as unresolved; the nuclear reaction network from Nuclear Forces and Nuclear Structure and Stellar Structure and Nucleosynthesis.]

Baryon acoustic oscillations

[Reserved: the same sound horizon imprinted on the galaxy distribution, first detected in the correlation function of luminous red galaxies [Eisenstein:2005]; its use as a standard ruler and the modern spectroscopic measurement [Adame:2025] — customarily dated to 2024 by its report number, though the journal issue is 2025; the consistency of the ruler with the microwave-background calibration as a further constraint on the composition.]

Structure formation

[Reserved: why structure cannot grow from the observed microwave-background fluctuations without a component that begins clustering before recombination [Peebles:1982]; the cold dark matter picture of hierarchical structure formation [Blumenthal:1984]; the universal halo density profile found in simulations [Navarro:1997]; large simulations reproducing the observed galaxy clustering [Springel:2005]; the honest counterweight — the core-cusp, missing-satellite and too-big-to-fail discrepancies on sub-galactic scales, which remain open and may be baryonic physics rather than a failure of the model.]

Candidates and the searches that found nothing

What a candidate must satisfy

[Reserved: the observational requirements — non-baryonic, cold or at least non-relativistic at decoupling, dissipationless, stable over the age of the universe, and electrically neutral; the thermal relic calculation, in which the observed abundance follows from a weak-scale annihilation cross-section [Lee:1977a], and why that coincidence motivated a generation of searches; the exclusion of Standard Model neutrinos as the dominant component by the free-streaming argument and by the mass bound of Experiment: Neutrino Oscillations; the candidate catalogue and its status [Bertone:2005].]

Direct detection: null results

[Reserved: the nuclear-recoil signature in an ultra-low background target, and the two current leading liquid-xenon experiments — LUX-ZEPLIN, with a spin-independent cross-section limit near \(9\times 10^{-52}\,\mathrm{m}^{2}\) at a mass of about \(36\,\mathrm{GeV}/c^{2}\) [Aalbers:2023], and XENONnT with a comparable limit [Aprile:2023]; four decades of improvement and no signal; the approaching neutrino fog, at which coherent solar and atmospheric neutrino scattering becomes an irreducible background; the flat statement that there is no detection.]

The DAMA claim and its non-confirmation

[Reserved: the annual modulation reported by DAMA/LIBRA in sodium iodide, at high statistical significance and with the phase expected from the Earth's motion through the halo [Bernabei:2008]; why it is inconsistent with the null results of Section 134.4.2 under standard halo and interaction assumptions; the same-target replications, which do not reproduce it [Adhikari:2018]; treated here as the worked example of how a positive claim is adjudicated rather than as evidence.]

Axions

[Reserved: the Peccei–Quinn mechanism proposed to solve the strong CP problem of Quantum Chromodynamics [Peccei:1977], and the light pseudoscalar it implies [Weinberg:1978] [Wilczek:1978]; why an axion is simultaneously a cold dark matter candidate; the microwave-cavity haloscope and the ADMX exclusion over the mass range near \(2.7\,\mu\mathrm{eV}\) to \(3.3\,\mu\mathrm{eV}\) at Dine–Fischler–Srednicki–Zhitnitsky coupling [Du:2018]; helioscope and light-shining-through-walls searches; again, no detection.]

Collider and indirect searches

[Reserved: the mono-jet plus missing transverse momentum signature at the Large Hadron Collider and its null result [Aad:2021]; the compilation of exclusion limits, including those on supersymmetric candidates [Navas:2024]; indirect searches for annihilation products in gamma rays, positrons and neutrinos, and the astrophysical backgrounds that limit them; the invisible-width bound on light candidates from Electroweak Unification and the Higgs Boson.]

Primordial black holes

[Reserved: black holes formed from early-universe density perturbations as a candidate requiring no new particle [Carr:1974]; the windows closed by microlensing [Tisserand:2007], by microwave-background accretion constraints and by the gravitational-wave merger rate of Experiment: Gravitational Waves; the asteroid-mass window that remains open; a fair statement of what fraction of the halo is still allowed.]

Modified dynamics as the rival hypothesis

MOND and the radial-acceleration relation

[Reserved: Milgrom's proposal that the discrepancy appears below an acceleration scale \(a_{0}\approx1.2\times 10^{-10}\,\mathrm{m}/\mathrm{s}^{2}\) rather than beyond a length scale, and the resulting flat rotation curves and baryonic Tully–Fisher relation [Milgrom:1983]; the tight empirical radial-acceleration relation between observed and baryonic centripetal acceleration across 153 galaxies [McGaugh:2016], which is a real regularity that any dark-matter model must also explain; the review that states the case at its strongest [Sanders:2002].]

Where modified dynamics fails

[Reserved: the residual mass discrepancy in clusters, roughly a factor of two, which MOND does not remove; the Bullet Cluster separation of lensing mass from baryons [Clowe:2006]; the relativistic completion TeVeS [Bekenstein:2004] and its prediction of a gravitational-wave propagation speed differing from \(c\), excluded to a part in \(10^{15}\) by GW170817 and its electromagnetic counterpart [Abbott:2017]; the microwave-background peak structure, which no modified-inertia theory has reproduced; the even-handed conclusion that the acceleration-scale regularity is unexplained by either side.]

Dark energy

The supernova evidence for acceleration

[Reserved: type Ia supernovae as standardizable candles after light-curve shape correction; the two independent teams' finding that distant supernovae are fainter than a decelerating universe allows [Riess:1998] [Perlmutter:1999]; the modern compilation with about 1550 supernovae and its systematic error budget [Brout:2022]; the deceleration parameter and the transition redshift near \(z\approx0.6\); the honest caveat about progenitor evolution and dust.]

The cosmological constant and its problem

[Reserved: \(\Lambda\) as the one term general relativity permits without new physics, introduced for a static universe [Einstein:1917a] and now measured as \(\Omega_{\Lambda}\approx0.685\) [Aghanim:2020]; the discrepancy between the observed value and any naive quantum-field-theoretic vacuum energy estimate, of order \(10^{120}\) [Weinberg:1989]; anthropic and multiverse arguments recorded as what they are — not testable by any experiment now conceivable — with the bound that started them [Weinberg:1987]; the connection to Quantum Gravity: The Honest Status.]

The equation of state

[Reserved: the parametrization \(w=p/\rho c^{2}\) and its constraint \(w=-1.03\pm0.03\) from the combination of supernovae, baryon acoustic oscillations and the microwave background [Aghanim:2020]; the recent spectroscopic hint of evolving \(w\) [Adame:2025], which is to be reported at its stated significance as a hint and not as a detection, since the preference depends on the supernova compilation combined with it; what a confirmed \(w\neq-1\) would and would not imply.]

Tensions and the honest status

The Hubble tension

[Reserved: the local distance-ladder value \(H_{0}=73.04(104)\,\mathrm{km}/\mathrm{s}/\mathrm{Mpc}\) [Riess:2022] against the microwave-background inference \(67.36(54)\,\mathrm{km}/\mathrm{s}/\mathrm{Mpc}\) [Aghanim:2020], a disagreement of about five standard deviations; the tip-of-the-red-giant-branch calibration, which lands between them and weakens the significance [Freedman:2021]; the possibilities — an unidentified systematic on either side, or new physics before recombination — stated without preference.]

The $S_{8}$ tension

[Reserved: weak-lensing surveys measuring slightly less clustering than the microwave background extrapolates [Asgari:2021] [Abbott:2022], at the two-to-three standard deviation level; the sensitivity of the comparison to baryonic feedback in the modelling and to intrinsic alignments; why a tension at this significance is reported and not yet believed.]

What is and is not known

[Reserved: the closing ledger. Established beyond reasonable doubt — that gravitating mass exceeds luminous mass by about five to one on every scale from galaxies to the observable universe, that most of it is non-baryonic [Aghanim:2020] [Cyburt:2016], that it is spatially separable from the baryons [Clowe:2006], and that the expansion is accelerating [Riess:1998] [Perlmutter:1999]. Not established — the identity of the dark matter, the nature of the acceleration, and whether either requires physics beyond general relativity. Forwarded to What We Observe but Do Not Understand.]