12.7 — Dark Matter and Dark Energy

Ninety-five percent of the universe is unidentified.

Component	Fraction	Status
Dark energy	68.5 %	Unknown
Dark matter	26.5 %	Unknown
Ordinary matter	4.9 %	Understood
Radiation	0.009 %	Understood

And of the 4.9 % that is ordinary matter, most is diffuse intergalactic gas. Stars are about 0.5 % of the universe's energy content. Everything you have ever seen, touched or measured directly is a rounding error.

This chapter takes both dark components seriously, sets out the full evidence, the candidates, the experiments, and the alternatives — including the ones that say the whole framework is wrong.

Dark matter: what it must be

Chapter 12.4 laid out six independent lines of evidence. From them, the properties are tightly constrained.

Dark. No electromagnetic interaction, or an extremely weak one. It does not emit, absorb, reflect or scatter light. This is the strongest constraint — any charged particle would have been seen.

Massive. It gravitates.

Cold. Non-relativistic when structure began forming.

Why cold matters. Relativistic particles stream out of small overdensities before they can collapse, erasing structure below a characteristic scale. Hot dark matter would produce a top-down universe — superclusters forming first and fragmenting — and the observed universe is bottom-up, with small galaxies forming first and merging.

\boxed{\text{Neutrinos are ruled out. They are too light, and therefore too fast.}}

With \sum m_\nu < 0.12 eV (Chapter 8.5), neutrinos contribute at most \Omega_\nu \approx 0.003 — under 1 % of the dark matter.

Collisionless. The Bullet Cluster constrains the self-interaction cross-section:

\frac{\sigma}{m} < 1\ \text{cm}^2/\text{g}

Stable. It has survived 13.8 billion years.

Non-baryonic. This is fixed by two independent measurements. Nucleosynthesis gives \Omega_bh^2 = 0.0224 from deuterium; the CMB gives \Omega_bh^2 = 0.0224 from the second peak height. Both are far below the total matter density.

Ruling out the boring answers

Before exotic particles, the ordinary possibilities were checked.

MACHOs — Massive Compact Halo Objects: faint stars, brown dwarfs, planets, black holes.

The test is gravitational microlensing. A compact object crossing in front of a background star magnifies it briefly, with a characteristic symmetric, achromatic light curve.

The MACHO and EROS surveys monitored millions of stars in the Magellanic Clouds for years.

Result: MACHOs account for under 20 % of the halo, and probably under 8 %. And they are baryonic anyway, so nucleosynthesis already excludes them as the bulk.

Cold gas — ruled out by absorption line surveys and by nucleosynthesis.

Primordial black holes remain marginally viable in narrow mass windows. Most ranges are excluded by microlensing (above 10^{-7}M_\odot), by CMB distortions from accretion, and by the absence of the Hawking evaporation bursts expected below 10^{12} kg (Chapter 12.3). The asteroid-mass window around 10^{17}–10^{22} kg is still open.

Candidates

WIMPs

Weakly Interacting Massive Particles, and the leading candidate for thirty years.

The WIMP miracle. Assume a stable particle of mass m with weak-scale interactions, in thermal equilibrium in the early universe. As the universe cools it freezes out, and the relic abundance is:

\Omega_\chi h^2 \approx \frac{3\times10^{-27}\ \text{cm}^3\text{/s}}{\langle\sigma v\rangle}

Plug in a weak-scale cross-section, \langle\sigma v\rangle \approx 3\times10^{-26} cm³/s:

\Omega_\chi h^2 \approx 0.1

\boxed{\text{Exactly the observed dark matter density, from weak-scale physics with no tuning.}}

This coincidence drove the field. And supersymmetry (Chapter 8.7) naturally provides a stable, neutral, weakly interacting particle — the lightest neutralino — with no extra assumptions.

Three detection strategies:

Direct detection. A WIMP passing through a detector occasionally recoils off a nucleus. The expected rate is under one event per kilogram per year, and the recoil energy is a few keV.

The experiments are deep underground to escape cosmic rays and use the cleanest materials ever made. LUX-ZEPLIN and XENONnT use multi-tonne liquid xenon targets, discriminating nuclear recoils from electron recoils by the ratio of scintillation light to ionisation charge.

Sensitivity has improved by a factor of 10^{6} since 2000.

Nothing has been found.

And the searches are approaching the "neutrino floor" — the point where coherent scattering of solar and atmospheric neutrinos produces an irreducible background that looks like a WIMP signal. Below that, direct detection becomes far harder.

Indirect detection. WIMPs annihilating in dense regions would produce gamma rays, positrons or neutrinos. Fermi-LAT looks at dwarf spheroidal galaxies, which are dark-matter dominated with few conventional gamma-ray sources.

The galactic centre shows an excess that fits a 30–50 GeV WIMP — and also fits a population of unresolved millisecond pulsars, which is now the favoured explanation.

Collider production. The LHC looks for events with large missing transverse momentum (Chapter 8.6). Nothing found, constraining WIMPs below about 1 TeV for standard couplings.

The honest assessment: the WIMP parameter space that motivated the field has been largely excluded. The idea is not dead — heavier or more weakly coupled WIMPs remain possible — but the miracle is no longer clean.

Axions

Now arguably the leading candidate, and it has a separate motivation.

The strong CP problem (Chapter 8.2). QCD permits a CP-violating term with a coefficient \theta that could be anything, and the neutron's electric dipole moment constrains it to |\theta| < 10^{-10}.

Peccei and Quinn proposed in 1977 that \theta is not a constant but a dynamical field, which naturally relaxes to zero. The associated particle is the axion, named by Wilczek after a detergent, because it cleaned up the problem.

Axion properties:

Very light — 10^{-6} to 10^{-3} eV in the favoured window, which is 10^{-11} times the electron mass.

Extremely weakly coupled.

And produced non-thermally by a misalignment mechanism, so despite being light they are cold — they were never in thermal equilibrium and have essentially no velocity dispersion.

The elegance is that the axion was not invented to be dark matter. It was invented to solve an unrelated problem in QCD and turns out to have the right properties.

Detection. Axions convert to photons in a strong magnetic field — the Primakoff effect.

ADMX uses a tunable microwave cavity in an 8 T magnet, cooled to 100 mK, scanning frequency slowly and looking for excess power. It has excluded parts of the favoured mass range.

IAXO will look for axions produced in the Sun.

And a coupling to nuclear spins is being searched for with nuclear magnetic resonance techniques.

Searches are ongoing and the parameter space is large.

Sterile neutrinos

A right-handed neutrino (Chapter 8.5) that does not feel the weak force, mixing only slightly with ordinary neutrinos.

A keV-scale sterile neutrino would be warm dark matter, which is between hot and cold and might help with the small-scale structure problems below.

A 3.5 keV X-ray line was reported in 2014 in stacked cluster spectra, consistent with sterile neutrino decay. Follow-up observations have not confirmed it and the favoured explanation is now an atomic line from potassium or argon.

Other candidates

Fuzzy dark matter — an ultralight scalar with m \sim 10^{-22} eV, giving a de Broglie wavelength of about a kiloparsec. The wave nature would suppress small-scale structure naturally.

Self-interacting dark matter — with a cross-section just below the Bullet Cluster limit, which would smooth out galactic cores.

Dark sector models — an entire hidden sector with its own forces and particles, coupling to ours only through gravity or a weak portal.

Small-scale problems

Cold dark matter simulations reproduce large-scale structure beautifully and have three persistent discrepancies at galaxy scales.

The core–cusp problem. Simulations predict density rising steeply towards galaxy centres — a cusp. Observations of dwarf galaxies show flat cores.

The missing satellites problem. Simulations predict hundreds of dwarf satellites around a Milky Way-sized galaxy. Far fewer are observed — though surveys keep finding more ultra-faint ones.

Too big to fail. The most massive predicted subhaloes are dense enough that they should have formed visible galaxies, and no observed satellite matches them.

Are these fatal? Probably not. All three involve the smallest scales, where ordinary baryonic physics — supernova feedback, stellar winds, reionisation heating — is hardest to model and has the largest effect. Simulations including realistic feedback have substantially reduced all three discrepancies.

But they are the strongest observational argument the alternatives have.

MOND and modified gravity

The alternative hypothesis: there is no dark matter, and gravity does not work as Newton and Einstein say at very low accelerations.

Mordehai Milgrom proposed MOND in 1983:

F = m\mu\!\left(\frac{a}{a_0}\right)a, \qquad a_0 \approx 1.2\times10^{-10}\ \text{m/s}^2

with \mu(x) \to 1 for x \gg 1 and \mu(x) \to x for x \ll 1.

In the low-acceleration regime:

\frac{GM}{r^2} = \frac{a^2}{a_0} \quad\Longrightarrow\quad a = \frac{\sqrt{GMa_0}}{r}

And for circular motion, a = v^2/r:

v^4 = GMa_0

\boxed{v = (GMa_0)^{1/4}}

Flat rotation curves, with no free parameter per galaxy.

What MOND gets right

This deserves acknowledgement, because it is often dismissed too quickly.

Rotation curves. MOND fits hundreds of galaxy rotation curves with one universal constant and the observed baryonic mass distribution. Dark matter fits require a halo profile with free parameters for each galaxy.

The baryonic Tully–Fisher relation. Observed:

M_{\text{baryonic}} \propto v^4

with remarkably little scatter, over five orders of magnitude in mass.

MOND predicts this exactly and with zero scatter, since it is the equation above rearranged. In the dark matter picture it is an emergent regularity that simulations struggle to reproduce this tightly.

Predictions that came true. Milgrom predicted in 1983 that low surface brightness galaxies would show large mass discrepancies. They were discovered later and do.

The radial acceleration relation. The observed acceleration in galaxies correlates tightly with the acceleration predicted from baryons alone, following a single curve. This is a MOND prediction and a puzzle for dark matter.

What MOND gets wrong

Galaxy clusters. MOND reduces the discrepancy but does not remove it. Clusters still need about a factor of 2 in unseen mass, so MOND requires dark matter anyway at that scale.

The Bullet Cluster. The lensing mass is displaced from the baryons (Chapter 12.4). In MOND the gravity should track the baryons. Relativistic versions of MOND have difficulty here, and this is generally considered the strongest single argument against it.

The CMB. The third acoustic peak's height is sensitive to the ratio of dark to baryonic matter. MOND without dark matter predicts a substantially different peak structure than is observed.

Structure formation. Without dark matter's head start (Chapter 12.4), forming the observed structure in 13.8 billion years is very difficult.

Gravitational wave speed. GW170817 showed gravity and light travel at the same speed to one part in 10^{15} (Chapter 6.10), which eliminated a large class of relativistic MOND theories overnight.

Where this leaves it

MOND is an excellent phenomenological description of galaxy dynamics and a failed cosmology.

The honest position is that MOND is telling us something real. The tightness of the radial acceleration relation is a genuine fact that dark matter models must explain, and "feedback conspires to produce it" is not fully satisfying.

And a_0 \approx cH_0/6 is a suspicious numerical coincidence, hinting at some connection between local dynamics and cosmology.

Most cosmologists hold that dark matter is real and that MOND has identified an unexplained regularity. A minority disagrees. The question is empirical and the experiments are running.

Dark energy

The second unknown, and the larger one.

The discovery

1998, two independent teams, the Supernova Cosmology Project and the High-Z Supernova Search Team.

The goal was to measure the deceleration. Everyone expected the expansion to be slowing under gravity; the question was by how much, and whether the universe would eventually recollapse.

The method: measure Type Ia supernovae (Chapter 12.2) at high redshift and compare their brightness with what a decelerating universe predicts.

The result: distant supernovae were fainter than expected, meaning further away, meaning the expansion has been accelerating.

Both teams checked exhaustively for systematics — dust, evolution of the supernova population, gravitational lensing — and the result held. Perlmutter, Schmidt and Riess shared the 2011 Nobel Prize.

And it has been confirmed by three independent routes since:

The CMB requires \Omega_{\text{total}} = 1 while matter is only 0.315, so something else makes up 0.685.

Baryon acoustic oscillations (Chapter 12.6) trace the expansion history and agree.

The age problem. Without dark energy, 1/H_0 = 14 Gy would be an overestimate of the age, giving about 9 Gy — younger than the oldest globular clusters at 12–13 Gy. Dark energy resolves it.

What it must be

The key parameter is the equation of state:

w = \frac{P}{\rho c^2}

From the second Friedmann equation (Chapter 12.5), acceleration requires:

\rho+\frac{3P}{c^2} < 0 \quad\Longrightarrow\quad w < -\frac{1}{3}

\boxed{\text{Dark energy has strongly negative pressure.}}

Measured:

w = -1.03 \pm 0.03

Consistent with exactly -1, which is a cosmological constant.

The candidates

A cosmological constant. \Lambda in the field equations (Chapter 6.8), interpreted as the energy density of the vacuum. w = -1 exactly, constant in space and time.

Its problem is severe. Chapter 7.9 computed the quantum field theory estimate:

\frac{\rho_{\text{predicted}}}{\rho_{\text{observed}}} \approx 10^{122}

The worst quantitative prediction in the history of science, and it has not improved since it was first noticed.

Quintessence. A dynamical scalar field slowly rolling down a potential, giving w slightly different from -1 and possibly varying with time.

It replaces one unexplained number with a field whose potential is also unexplained, and current data cannot distinguish it from \Lambda.

Modified gravity on cosmological scales. Perhaps general relativity is wrong at the largest scales rather than there being a new substance. Constrained heavily by GW170817 and by solar system tests.

We are misinterpreting the data. Perhaps large-scale inhomogeneity mimics acceleration. Studied carefully and found insufficient.

The coincidence problem

Dark energy density is constant; matter density falls as a^{-3} (Chapter 12.5).

They were equal at about 9.8 billion years, and we are at 13.8.

\boxed{\text{Why do we live at the one epoch when the two are comparable?}}

Earlier and matter dominates completely; later and dark energy does. The crossover occupies a small fraction of cosmic history and we are in it.

Proposed responses:

Coincidence. Possible, and unsatisfying.

Anthropic selection. If \Lambda were much larger, the universe would have started accelerating before galaxies formed, and there would be no observers. Weinberg made this argument in 1987 and predicted a small non-zero \Lambda before it was measured — a rare case of anthropic reasoning making a successful prediction. It requires a multiverse to be meaningful (Chapter 12.9).

Quintessence models designed so that the field naturally tracks the matter density.

Unresolved.

Recent developments

DESI, the Dark Energy Spectroscopic Instrument, released results in 2024 and 2025 measuring baryon acoustic oscillations across many redshifts with unprecedented precision.

Combined with supernovae and the CMB, the data show a preference — at about 2.8 to 4.2 sigma depending on the dataset combination — for dark energy that is evolving, with w having been below -1 in the past and rising towards -1 or above now.

If confirmed, this rules out a pure cosmological constant.

It is not confirmed. The significance depends on which supernova compilation is used, and Chapter 8.6's cautionary tales apply. Euclid, the Vera Rubin Observatory and the Nancy Grace Roman Telescope will settle it within a decade.

This is currently the most interesting live question in cosmology.

Where this shows up in your life

Nowhere directly, and that is worth saying honestly. Dark matter and dark energy have no applications and probably never will.

What they represent is the scale of what is not understood. A theory that describes 5 % of the universe's energy content is not a complete theory, however precisely it describes that 5 %.

And the technology developed to look for them — ultra-low-background detectors, large-scale sky surveys, precision spectroscopy — feeds into medical imaging, materials analysis, nuclear security and machine learning on very large datasets.

The detectors built to find dark matter are now the most sensitive neutrino detectors in existence, and in 2024 XENONnT observed coherent neutrino–nucleus scattering from solar neutrinos for the first time — a Standard Model process predicted in 1974 and never before seen at those energies.

What the next chapter fixes

The contents are measured and mostly unidentified. The geometry and the future are separate questions, and they turn out to be less connected than they were once thought. Chapter 12.8 covers the shape of space, the difference between the observable universe and the universe, the horizons that determine what can ever be known, and where all of this ends — including the calculation of when the last star goes out.