Dark matter and dark energy: evidence, candidates, and the accelerating expansion

Intuition Beginner

Everything we can see — stars, planets, gas, dust, and us — makes up only about 5% of the universe. Another 27% is dark matter: invisible stuff that we cannot see directly but whose gravity holds galaxies together and shapes the cosmic web. The remaining 68% is dark energy, a mysterious force pushing the universe apart. Ninety-five percent of the cosmos is made of things we have never seen in a laboratory.

We know dark matter exists because galaxies rotate too fast to be held together by visible matter alone. If only the stars and gas we can see were pulling, the outer parts of galaxies would fly off. They do not, which means something unseen adds extra gravity. Clusters of galaxies also bend light far more than their visible mass can explain, a second line of evidence called gravitational lensing.

Dark energy is stranger still. In 1998, two teams studying distant supernovae discovered that the universe's expansion is speeding up, not slowing down as everyone expected. Whatever dark energy is, it now dominates the cosmos and decides its fate. Astronomers still do not know what dark matter or dark energy are made of — only that they must be there.

Visual Beginner

Component	Share of universe	What it does
Dark energy	~68%	Pushes space apart; accelerates expansion
Dark matter	~27%	Adds gravity; binds galaxies and clusters
Ordinary matter	~5%	Atoms; everything we can see or touch

Together, dark matter and dark energy make up about 95% of the universe. Ordinary matter — every star, planet, and person — is a thin residue.

Evidence	What it shows	Key object or probe
Galaxy rotation curves	Stars move too fast at the edge	Vera Rubin's spirals
Gravitational lensing	Mass bends light more than stars can	Bullet Cluster 1E 0657-558
Cosmic microwave background	Counts dark and ordinary matter separately	Planck acoustic peaks
Type Ia supernovae (1998)	Distant supernovae are too dim	Acceleration discovery
Large-scale structure	Cosmic web needs cold dark matter	Galaxy surveys, BAO

Worked example Beginner

Example 1: The outer stars that should have flown away

The Sun orbits the centre of the Milky Way at about 220 km/s, roughly 26,000 light-years out. If the galaxy's mass ended where its visible starlight ends, a star twice as far out should travel much slower, about 220 divided by the square root of 2, or 155 km/s. Instead, observed stars at that distance still move at about 220 km/s. For the speed to stay flat, the enclosed mass must keep growing with radius, long past the glowing disk. That extra, unseen mass is the dark matter halo.

Example 2: Reading the cosmic budget

Of the universe's total energy, ordinary matter is about 5%, dark matter about 27%, and dark energy about 68%. How much is "dark", meaning we cannot see or explain it? Add the dark matter and dark energy shares: 27 plus 68 equals 95. So only 5 percent of the cosmos is matter we understand. How many times more dark matter is there than ordinary matter? Divide 27 by 5, giving roughly five and a half. There is over five times as much dark matter as the matter we are made of.

Example 3: Why faint supernovae meant acceleration

Type Ia supernovae all reach nearly the same peak brightness, so they act as standard candles: compare how faint one looks and you learn its distance. In a universe whose expansion is slowing, distant supernovae would appear brighter than in a coasting one, because gravity would have held them closer. The 1998 teams found the opposite — distant supernovae were about a quarter of a magnitude too dim, meaning they were farther away than any decelerating model allowed. The only way they could be pushed that far is if the expansion sped up. Two independent teams agreed, and the case for dark energy was made.

Check your understanding Beginner

Formal definition Intermediate+

Density parameters and the cosmic inventory

The energy contents of the universe are encoded in dimensionless density parameters ${\Omega }_i\equiv {\rho }_i/{\rho }_{\mathrm{crit}}$, where the critical density

$${\rho }_{\mathrm{crit}}=\frac{3H_0^2}{8\pi G}\approx 1.88\times 10^{-26}\mathrm{kg}{\mathrm{m}}^{-3}\approx 8.6\times 10^{-27}\mathrm{kg}{\mathrm{m}}^{-3}$$

(for $H_0\approx 67.4\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$) sets the boundary between a closed and open universe. The present-day inventory is ${\Omega }_b\approx 0.049$ (baryons), ${\Omega }_c\approx 0.265$ (cold dark matter), ${\Omega }_{\Lambda }\approx 0.685$ (dark energy), ${\Omega }_r\approx 5\times 10^{-5}$ (radiation), with ${\Omega }_b+{\Omega }_c+{\Omega }_{\Lambda }\approx 1$ consistent with spatial flatness. Cold dark matter outweighs baryonic matter by roughly five to one.

Galaxy rotation curves and the dark halo

For a test particle on a circular orbit at radius $r$ in a spherically symmetric mass distribution, balancing centripetal acceleration against gravity gives

$$v_c^2(r)=\frac{GM(<r)}{r},M(<r)=4\pi {\int }_0^r\rho (r^{\prime })r^{\prime 2}d{r}^{\prime }.$$

The visible component of a spiral galaxy — stars and gas — is concentrated in a thin exponential disk whose surface brightness falls off as $I(R)\propto \exp (-R/R_d)$. Beyond a few disk scale lengths the luminous mass converges, so Keplerian behaviour $v_c\propto r^{-1/2}$ is expected. Vera Rubin and Kent Ford's observations (1970s–80s) showed instead that $v_c(r)$ stays flat, often out to the last measured point. A flat curve $v_c=v_0$ forces $M(<r)=v_0^{2}r/G\propto r$, so mass continues to accumulate far beyond the luminous disk. The discrepancy is parametrized by the mass-to-light ratio $M/L$, which climbs from $\sim 5M_{\odot }/L_{\odot }$ in the inner disk to $\sim 100M_{\odot }/L_{\odot }$ in the outer halo.

The canonical NFW profile (Navarro, Frenk, White), predicted by cold-dark-matter simulations, describes the halo density,

$${\rho }_{\mathrm{NFW}}(r)=\frac{{\rho }_s}{(r/r_s)(1+r/r_s{)}^2},$$

which diverges as $r^{-1}$ at small radius (a "cusp") and falls as $r^{-3}$ at large radius. Observed dwarf and low-surface-brightness galaxies often prefer cores over cusps, the cusp-core problem, a possible signature of baryonic feedback or of non-cold dark matter.

Gravitational lensing: strong, weak, and the Bullet Cluster

A mass concentration deflects light. For a point lens the Einstein radius is

$${\theta }_E=\sqrt{\frac{4GM}{c^2}\frac{D_{LS}}{D_L{D}_S}},$$

where $D_L,D_S,D_{LS}$ are angular-diameter distances. When the source lies close to the line of sight, strong lensing produces arcs, multiple images, and Einstein rings, from which the enclosed mass is read off geometry alone, independent of luminosity. In the weak-lensing regime, the shapes of background galaxies are statistically sheared by a few percent; the convergence

$$\kappa =\frac{\Sigma }{{\Sigma }_{\mathrm{crit}}},{\Sigma }_{\mathrm{crit}}=\frac{c^2}{4\pi G}\frac{D_S}{D_L{D}_{LS}},$$

maps the projected surface mass density $\Sigma$ across the field.

The Bullet Cluster (1E 0657-558) is the most direct single example. Two galaxy clusters have passed through each other; the hot X-ray-emitting baryonic gas — most of the ordinary mass — is shocked and lagged by ram pressure, sitting between the two galaxy concentrations. Weak-lensing reconstruction places the bulk of the mass not on the gas but on the two galaxy clumps, which sailed through collisionlessly. The mass and the luminous baryons are spatially separated, which modified-gravity theories without dark matter struggle to reproduce.

CMB and large-scale structure evidence

The CMB acoustic peaks (28.04.03) separately fix ${\Omega }_b{h}^2$ and ${\Omega }_c{h}^2$: baryons add inertia to the photon-baryon oscillator and boost odd peaks, while cold dark matter contributes gravity without pressure and sets the overall peak height and the early Integrated Sachs-Wolfe effect. Planck infers ${\Omega }_c{h}^2=0.120\pm 0.001$, about five times the baryon density. The flat geometry ${\Omega }_k\approx 0$ combined with the matter density ${\Omega }_m\approx 0.315$ forces a large non-matter component, ${\Omega }_{\Lambda }\approx 0.685$, even before the supernova data are invoked.

Large-scale structure provides two further handles. The baryon acoustic oscillation (BAO) feature — the same sound-horizon ruler imprinted on the galaxy power spectrum — measures the distance-redshift relation $D_V(z)$, and galaxy cluster counts and weak-lensing tomography constrain the growth of structure, which depends on ${\Omega }_m$ and is suppressed by dark energy at late times.

Dark matter candidates and detection

The leading candidates are:

• WIMPs (Weakly Interacting Massive Particles), masses $\sim 10\mathrm{GeV}$ to $100\mathrm{TeV}$, with electroweak-scale couplings. A thermal relic freezes out when the annihilation rate drops below the expansion rate, giving a cross section $⟨\sigma v⟩\approx 3\times 10^{-26}\mathrm{c}{\mathrm{m}}^3{\mathrm{s}}^{-1}$ that yields ${\Omega }_c\sim 0.2$ almost independently of mass — the WIMP miracle. SUSY neutralinos are the canonical realization.
• Axions, ultralight ($\sim 10^{-5}\mathrm{eV}$), arising from the Peccei-Quinn solution to the strong CP problem; detected by cavity haloscopes (ADMX).
• Sterile neutrinos in the keV range, a warm-dark-matter candidate with small-scale cutoffs.
• Primordial black holes, constrained by microlensing, CMB accretion, and pulsar timing.

Detection strategies are three-pronged. Direct detection records the nuclear recoil from a Galactic WIMP scattering in a detector: XENON1T/nT, LUX-ZEPLIN, and PandaX use multi-tonne liquid xenon, with current spin-independent cross-section limits near $10^{-47}\mathrm{c}{\mathrm{m}}^2$ at $30\mathrm{GeV}$. Indirect detection searches for annihilation or decay products — gamma rays (Fermi-LAT), neutrinos (IceCube, ANTARES, KM3NeT), and antimatter (AMS-02). Collider production at the LHC looks for missing transverse energy. No confirmed detection has yet been made.

Dark energy: equation of state and the Friedmann equations

Dark energy is parametrized by its equation-of-state parameter

$$w\equiv \frac{p}{\rho c^2}.$$

The energy density of a component with constant $w$ redshifts as $\rho \propto a^{-3(1+w)}$. The Friedmann equation for a flat universe reads

$$H^2(a)=H_0^2[{\Omega }_m{a}^{-3}+{\Omega }_r{a}^{-4}+{\Omega }_{\mathrm{DE}}{a}^{-3(1+w)}],$$

with the curvature term ${\Omega }_k{a}^{-2}$ added in the non-flat case. A cosmological constant has $w=-1$ and ${\rho }_{\Lambda }=\mathrm{const}$, contributing ${\Omega }_{\Lambda }$ independent of $a$. Quintessence ($-1<w<0$) has a density that slowly decays; phantom energy ($w<-1$) has a density that grows with expansion and ends in a Big Rip.

The acceleration is governed by the Raychaudhuri (second Friedmann) equation,

$$\frac{\ddot{a}}{a}=-\frac{4\pi G}{3}\sum _i\left({\rho }_i+\frac{3p_i}{c^2}\right)=-\frac{4\pi G}{3}\sum _i{\rho }_i(1+3w_i).$$

A component drives acceleration when $w<-1/3$, violating the strong energy condition. Radiation ($w=1/3$) and matter ($w=0$) decelerate; only dark energy with $w\approx -1$ accelerates.

Type Ia supernovae and the accelerating expansion

Type Ia supernovae have a calibrated peak luminosity (via the Phillips relation between peak brightness and light-curve width), making them standardizable candles. Their distance modulus

$$\mu =m-M=5{\log }_{10}\left(\frac{d_L}{10\mathrm{pc}}\right)$$

depends on the luminosity distance $d_L(z)$, which is itself an integral over the expansion history,

$$d_L(z)=(1+z)c{\int }_0^z\frac{d{z}^{\prime }}{H(z^{\prime })}$$

(for a flat universe). In an accelerating universe $d_L$ is larger at given $z$ than in a decelerating or coasting one, so supernovae appear dimmer. The High-z Supernova Search Team (Riess, Schmidt, Kirshner) and the Supernova Cosmology Project (Perlmutter) independently found just this: high-redshift supernovae were $\sim 0.25\mathrm{mag}$ fainter than the ${\Omega }_{\Lambda }=0$ prediction, requiring ${\Omega }_{\Lambda }>0$.

Key result: the LCDM concordance model Intermediate+

Combining the CMB acoustic peaks (28.04.03), the BAO distance scale, and the Type Ia supernova Hubble diagram yields the spatially-flat $\Lambda$CDM concordance model. The three data sets are complementary: the CMB fixes the physical densities ${\Omega }_b{h}^2$ and ${\Omega }_c{h}^2$ and the angular sound horizon, BAO measures the distance-redshift relation at intermediate $z$, and the supernovae are most sensitive to the acceleration and hence to ${\Omega }_{\Lambda }$ at low $z$. Plotted together on the ${\Omega }_m$-${\Omega }_{\Lambda }$ plane they form the cosmic triangle, three nearly orthogonal constraint bands meeting at a single point.

The Planck 2018 baseline plus BAO best-fit values are

$${\Omega }_m=0.3153\pm 0.0007,{\Omega }_{\Lambda }=0.6847\pm 0.0007,$$ $$H_0=67.36\pm 0.54\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1},w=-1.03\pm 0.03,$$

with the cold dark matter density ${\Omega }_c{h}^2=0.120\pm 0.001$ and the baryon density ${\Omega }_b{h}^2=0.0224\pm 0.0001$. The deceleration parameter is $q_0={\Omega }_m/2-{\Omega }_{\Lambda }\approx -0.53$, confirming acceleration at high significance. The equation of state is consistent with a cosmological constant, $w=-1$, to a few percent.

Two cross-checks anchor the result. First, the baryon density from the CMB matches the Big Bang nucleosynthesis value from primordial deuterium (28.04.02) to within a few percent, a concordance spanning nine orders of magnitude in time. Second, the spatial curvature ${\Omega }_k=0.0007\pm 0.0019$ is consistent with flatness, so ${\Omega }_{\Lambda }=1-{\Omega }_m$ is fixed once ${\Omega }_m$ is measured. The dark sector — $\sim 95\%$ of the universe — is thus pinned down to a few percent precision by geometry, even though its microphysical nature remains unknown.

Exercises Intermediate+

Advanced results Master

Friedmann equations with $\Lambda$ and the condition for acceleration

For a flat Friedmann-Lemaitre-Robertson-Walker universe the two governing equations are

$$H^2={\left(\frac{\dot{a}}{a}\right)}^2=\frac{8\pi G}{3}\rho -\frac{k{c}^2}{a^2}+\frac{\Lambda c^2}{3},\frac{\ddot{a}}{a}=-\frac{4\pi G}{3}\left(\rho +\frac{3p}{c^2}\right)+\frac{\Lambda c^2}{3}.$$

Introducing density parameters ${\Omega }_i={\rho }_i/{\rho }_{\mathrm{crit}}$ and absorbing $\Lambda$ as ${\rho }_{\Lambda }=\Lambda c^2/(8\pi G)$ with $w=-1$, the first equation becomes $H^2/H_0^2={\Omega }_m{a}^{-3}+{\Omega }_r{a}^{-4}+{\Omega }_k{a}^{-2}+{\Omega }_{\Lambda }$. The acceleration equation for a flat matter-plus-$\Lambda$ universe gives the deceleration parameter

$$q_0\equiv -\frac{\ddot{a}a}{{\dot{a}}^2}{|}_0=\frac{{\Omega }_m}{2}-{\Omega }_{\Lambda },$$

so the universe accelerates ($\ddot{a}>0$, $q_0<0$) when ${\Omega }_{\Lambda }>{\Omega }_m/2$. In a flat universe this is ${\Omega }_{\Lambda }>1/3$; the transition redshift at which $\ddot{a}$ changed sign, solving ${\Omega }_{\Lambda }={\Omega }_m(1+z{)}^3/2$, is $z_t\approx 0.60$. The observed ${\Omega }_m\approx 0.315$, ${\Omega }_{\Lambda }\approx 0.685$ gives $q_0\approx -0.53$: we live in the accelerating phase, which began roughly five billion years ago.

The cosmological constant problem

Quantum field theory assigns every mode of every field a zero-point energy $\frac{1}{2}\hslash \omega$ per mode, giving a vacuum energy density that naively diverges. Cutting off at the Planck scale yields ${\rho }_{\mathrm{vac}}\sim M_{\mathrm{Pl}}^4\sim 10^{112}\mathrm{e}{\mathrm{V}}^4$, whereas the observed dark energy density is ${\rho }_{\Lambda }\sim (2\mathrm{meV}{)}^4\sim 10^{-47}\mathrm{Ge}{\mathrm{V}}^4$. The discrepancy is roughly $10^{120}$ — widely called the worst prediction in physics. Even a cutoff at the electroweak scale overshoots by $\sim 10^{55}$. Supersymmetry, if exact, would cancel bosonic and fermionic zero-point contributions exactly, but supersymmetry is broken at $\gtrsim \mathrm{TeV}$ scales, leaving a residual $\sim 10^{55}$ discrepancy. Whether ${\rho }_{\Lambda }$ is a true constant (in which case the smallness demands an anthropic or symmetry explanation) or a dynamical quintessence field (evading the problem by construction) is open.

Quintessence, phantom energy, and the Big Rip

A canonical scalar field $\varphi$ with potential $V(\varphi )$ has equation of state

$$w_{\varphi }=\frac{\frac{1}{2}{\dot{\varphi }}^2-V(\varphi )}{\frac{1}{2}{\dot{\varphi }}^2+V(\varphi )},$$

ranging from $w=+1$ (kinetic-dominated) to $w=-1$ (potential-dominated). Slow-roll down a very flat potential ("Ratra-Peebles" or "tracker" quintessence) yields $w\approx -0.9$ today, with $w(a)$ time-varying and potentially distinguishable from $\Lambda$ by next-generation surveys. Phantom fields ($w<-1$) require a negative kinetic term; their density grows with expansion, the scale factor diverges in finite proper time, and bound structures — clusters, galaxies, solar systems, atoms — are torn apart in a Big Rip at $t_{\mathrm{rip}}\approx 2H_0^{-1}/[3|1+w|]$ before the present for $w$ near $-1.5$. Current combined constraints give $w_0=-1.03\pm 0.03$, consistent with $\Lambda$ but not excluding mild quintessence.

Cosmological parameter constraints: the cosmic triangle

The ${\Omega }_m$-${\Omega }_{\Lambda }$ plane hosts three near-orthogonal constraints. The CMB fixes the angular sound horizon ${\theta }_{\ast }$, giving a thin ridge along the flat line ${\Omega }_m+{\Omega }_{\Lambda }=1$ and breaking degeneracies via peak heights. BAO measures $D_V(z)/r_s$ at several redshifts, giving stripes of constant distance roughly perpendicular to the supernova contours. Type Ia supernovae measure $d_L(z)$, giving bands of constant luminosity distance. The three intersect in a small triangle near ${\Omega }_m\approx 0.3$, ${\Omega }_{\Lambda }\approx 0.7$; the consistency of three independent geometrical probes is the backbone of the concordance model. Adding the growth-of-structure measurements (weak lensing, cluster counts, redshift-space distortions) tests whether the same ${\Omega }_m$ governs both geometry and the growth rate $f{\sigma }_8$.

The Hubble tension

Planck's $H_0=67.36\pm 0.54\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$ disagrees with the SH0ES distance-ladder value $H_0=73.0\pm 1.0\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$ (Riess et al., calibrated on Large Magellanic Cloud Cepheids) at $4$–$5\sigma$. The tension is robust to every reanalysis within $\Lambda$CDM and to every step of the ladder (Cepheids, the maser distance to NGC 4258, the tip-of-the-red-giant-branch method). Possible resolutions split into systematics (a hidden distance-ladder bias, though none has survived scrutiny) and new physics: early dark energy raising $H_0$ by shrinking the sound horizon, additional relativistic species ($\Delta N_{\mathrm{eff}}$), interacting dark sectors, or a time-varying $w(a)$. Each solution tends to fix $H_0$ only at the cost of worsening ${\sigma }_8$ or $S_8$ constraints, and none has consensus.

Structure formation and the ${\sigma }_8$ tension

Linear perturbation theory in $\Lambda$CDM gives the growth of matter fluctuations $\delta (a)={\delta }_m(\mathbf{x},a)/{\bar{\rho }}_m$ via

$$\ddot{\delta }+2H\dot{\delta }-4\pi G{\rho }_m\delta =0,$$

with growing-mode solution $\delta \propto D(a)$, where in the matter era $D\propto a$ and at late times dark energy suppresses growth relative to $a$. The growth rate $f=d\ln D/d\ln a\approx {\Omega }_m(a{)}^{\gamma }$ with $\gamma \approx 0.55$ for $\Lambda$CDM is measured by redshift-space distortions. The amplitude ${\sigma }_8$ — the rms fluctuation in $8\mathrm{Mpc}/h$ spheres — is inferred by Planck as ${\sigma }_8=0.811$, but weak-lensing surveys (KiDS, DES) and cluster counts prefer $S_8\equiv {\sigma }_8\sqrt{{\Omega }_m/0.3}\approx 0.76$, a $2$–$3\sigma$ ${\sigma }_8$ tension. Transfer functions (BBKS, Eisenstein-Hu) encode the shape of the linear power spectrum $P(k)$, with the turnover at $k_{\mathrm{eq}}$ fixing ${\Omega }_{m}h$.

Dark energy surveys and future constraints

The Dark Energy Survey (DES), the ESA Euclid mission (launched 2023), and the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) target percent-level measurements of $w_0$ and $w_a$ via weak lensing, BAO, supernovae, and cluster counts. Euclid alone forecasts $\sigma (w_0)\approx 0.03$ and $\sigma (w_a)\approx 0.1$ from a combination of weak lensing and galaxy clustering out to $z\sim 2$. The figure of merit $\propto [\det \mathrm{Cov}(w_0,w_a){]}^{-1}$ quantifies the ability to distinguish $\Lambda$ from quintessence. The Nancy Grace Roman Space Telescope will contribute a supernova Hubble diagram out to $z\sim 2.5$ with thousands of Type Ia events.

Modified gravity alternatives

If dark energy is geometric rather than material, one may modify general relativity on cosmological scales. $f(R)$ gravity replaces the Einstein-Hilbert action with a function of the Ricci scalar; viable models (Hu-Sawicki, Starobinsky) mimic $\Lambda$CDM at late times but introduce a scalaron, constrained by solar-system tests via the chameleon mechanism. DGP braneworld gravity puts our universe on a brane in a five-dimensional bulk, producing late-time acceleration from the modification itself; it is disfavoured by its predicted growth-suppression and by the integrated Sachs-Wolfe effect. TeVeS (Bekenstein's tensor-vector-scalar theory) was devised to reproduce MOND phenomenology and to reproduce galaxy rotation curves without dark matter, but it fails on cluster scales (the Bullet Cluster especially) and is essentially excluded by gravitational-wave event GW170817, which confirmed $c_g=c$ to one part in $10^{15}$. No modified-gravity model yet reproduces the full $\Lambda$CDM concordance without a dark sector.

The Bullet Cluster as direct proof

Clowe, Gonzalez, and Markevitch (2006, ApJ 648, L109) titled their paper "A direct empirical proof of the existence of dark matter." Their weak-lensing mass map of the Bullet Cluster (1E 0657-558) shows two mass concentrations coincident with the collisionless galaxies, displaced by Machacek-style ram pressure from the bulk of the baryons (the X-ray gas). The gas-to-mass ratio of the cluster, measured separately, shows the baryon fraction dropping from $\sim 15\%$ in the gas-rich centre to $\ll 1\%$ at the mass peaks. The spatial offset is quantitatively inconsistent with any theory that ties the gravitational field to the visible matter distribution. The Bullet Cluster remains the single most persuasive piece of evidence that dark matter is a substance rather than a law-of-gravity correction.

The WIMP miracle, self-interacting, and ultralight dark matter

The thermal relic cross section follows from freeze-out: when $\Gamma =n⟨\sigma v⟩$ falls below $H$, the comoving abundance is fixed. Matching ${\Omega }_c{h}^2\approx 0.12$ requires $⟨\sigma v⟩\approx 3\times 10^{-26}\mathrm{c}{\mathrm{m}}^3{\mathrm{s}}^{-1}$, which coincides with the electroweak cross section for a weakly interacting $\sim 100\mathrm{GeV}$ particle — the WIMP miracle and its link to supersymmetry. The null results from XENON1T, LUX-ZEPLIN, and PandaX now exclude much of the natural WIMP parameter space below $\sim 100\mathrm{GeV}$, motivating alternatives. Self-interacting dark matter (SIDM) postulates a dark-sector self-coupling $\sigma /m\sim 0.1$–$1\mathrm{c}{\mathrm{m}}^2{\mathrm{g}}^{-1}$ that thermalizes halo cores and resolves the cusp-core and too-big-to-fail problems. Fuzzy (ultralight) dark matter takes the particle mass down to $\sim 10^{-22}\mathrm{eV}$, where the de Broglie wavelength is galactic and the dark matter behaves as a Bose-Einstein condensate with a Jeans scale that suppresses small-scale structure; this predicts solitonic cores in dwarf galaxies but is strained by Lyman-$\alpha$ forest constraints.

Dark sector theories

A broader class of models endows dark matter with its own forces and particles — a dark sector. A massless dark photon kinetically mixed with the Standard Model photon introduces long-range dark forces; dark acoustic oscillations arise if dark radiation couples to dark matter before recombination, leaving imprints in the matter power spectrum analogous to baryon acoustic oscillations; strongly interacting dark sectors admit dark composites (dark nuclei) and dissipative dark matter that can form dark disks. These models are tested by their effects on the CMB damping tail, small-scale structure, direct-detection spectra, and the self-interaction bounds from the Bullet Cluster and from cluster shapes.

Connections Master

Connections to the Big Bang and cosmic expansion (28.04.01)

Dark energy is the engine behind the late-time acceleration introduced in 28.04.01, and it alone decides the universe's fate. With $w=-1$ the expansion continues forever toward a cold, empty heat death; with $w<-1$ a Big Rip tears apart bound structures; with a decaying quintessence the universe may recollapse. The 1998 supernova result transformed the open question of the fate of the universe into a measurement of the dark energy equation of state, and the cosmological-constant problem it raised is among the deepest open questions linking cosmology to quantum field theory.

Connections to the cosmic microwave background (28.04.03)

The CMB fixes the dark matter and dark energy densities by independent channels. Cold dark matter is required to produce the observed acoustic peak amplitudes and positions; without it the second peak is far too low and the early formation of structure cannot proceed. The dark energy density follows from the angular-diameter distance to last scattering and the flatness constraint. The Hubble tension — Planck's $H_0=67.4$ versus the local $73.0$ — is a discrepancy between the early-universe value inferred from the CMB within $\Lambda$CDM and the late-universe value measured locally, and is the most active interface between CMB cosmology and dark-sector physics.

Connections to Big Bang nucleosynthesis (28.04.02)

Big Bang nucleosynthesis fixes the baryon density ${\Omega }_b{h}^2\approx 0.0224$ from the primordial deuterium abundance, a value that matches the CMB-inferred baryon density to within a few percent across nine orders of magnitude in cosmic time. The remaining matter — the five-times-larger cold dark matter component — is nonbaryonic by construction: it neither participated in nuclear reactions nor coupled to the photon bath, leaving BBN unchanged while dominating the gravitational budget. The dark matter must therefore be a new particle outside the Standard Model.

Connections to galaxies and galaxy structure (28.03)

Galaxy rotation curves (28.03.01, 28.03.02) are the most direct dynamical evidence for dark matter on galactic scales. The NFW halo profile, the cusp-core problem, and the baryonic Tully-Fisher relation link the dark and luminous components of galaxies. Active galactic nuclei (28.03.03) sit in supermassive black holes whose growth is regulated by the same halo potential wells that dark matter establishes. The inferred dark matter distribution from rotation curves, lensing, and satellite kinematics must be consistent with the halos produced in $\Lambda$CDM simulations.

Connections to particle physics and quantum field theory

Dark matter candidates and the cosmological constant problem are at root questions of particle physics. WIMPs link cosmology to supersymmetry and to collider searches at the LHC; axions tie the dark matter to the strong CP problem and the Peccei-Quinn mechanism; sterile neutrinos invoke seesaw extensions of the Standard Model. The cosmological constant problem is a direct confrontation between quantum field theory's prediction of vacuum energy and general relativity's response to it — the failure of the naive prediction by $10^{120}$ is the sharpest known tension between the two foundational theories.

Historical and philosophical context Master

Zwicky and the missing mass

In 1933 the Swiss astronomer Fritz Zwicky applied the virial theorem to the Coma cluster and found that the galaxies moved far too fast to be bound by their luminous mass. He inferred the presence of dunkle Materie — dark matter — exceeding the visible matter by a factor of hundreds (his estimate was high because he underestimated the distance to Coma). The result was ignored for decades, partly because Zwicky was a difficult colleague and partly because the very notion of unseen mass on cluster scales had no independent support.

Vera Rubin and the rotation curves

Vera Rubin and Kent Ford, working at the Carnegie Institution from the late 1960s, obtained long-slit spectra of dozens of spiral galaxies with a new image-tube spectrograph. By 1978 they had shown that rotation curves remained flat far beyond the optical disk in every case. Combined with Morton Roberts's independent radio hydrogen measurements, the evidence for extended dark halos became overwhelming. Rubin's persistence turned a cluster-scale curiosity into a galactic-scale fact, and dark matter passed from speculation to orthodoxy.

Einstein's cosmological constant

Einstein introduced $\Lambda$ in 1917 to allow a static cosmological solution to his field equations, then abandoned it as his "biggest blunder" after Hubble discovered the expansion in 1929. The term never disappeared from the theory — it is a perfectly valid integration constant — but it was widely assumed to be zero until the late 1990s. The 1998 supernova result resurrected it with a small positive value, vindicating the mathematical possibility Einstein had discarded and giving the universe a cosmological constant roughly $10^{120}$ times smaller than naïve quantum-field-theoretic arguments predict.

The 1998 discovery

Saul Perlmutter's Supernova Cosmology Project at Berkeley and the High-z Supernova Search Team led by Brian Schmidt and Adam Riess independently built pipelines to discover and measure Type Ia supernovae out to redshift $z\sim 1$. Both teams found that distant supernovae were systematically dimmer than a $\Lambda =0$ universe would predict. Riess et al. published in September 1998 (Astronomical Journal 116, 1009), Perlmutter et al. in June 1999 (Astrophysical Journal 517, 565), and their conclusions agreed: the universe's expansion is accelerating. Perlmutter, Schmidt, and Riess shared the 2011 Nobel Prize in Physics. The result inverted cosmology's default expectation — that gravity was slowing the expansion — and made dark energy the dominant component of the cosmos.

The naming of dark energy

"Dark matter" descends directly from Zwicky's dunkle Materie. "Dark energy" was coined in 1998, shortly after the supernova result, by Michael Turner (and independently by Dragan Huterer and Turner), to distinguish the smoothly distributed, gravitationally repulsive component from particulate dark matter. The name reflects our ignorance: "dark" because it is unseen, "energy" because it behaves as a uniform energy density with negative pressure rather than as a clumping substance. Whether dark energy is a true cosmological constant, a dynamical scalar field, or a sign that gravity itself must be modified on the largest scales remains the central open question of cosmology.

Bibliography Master

1. Zwicky, F. (1933). "Die Rotverschiebung von extragalaktischen Nebeln." Helvetica Physica Acta, 6, 110-127.

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