---
title: Dark Matter, Dark Energy, and Open Questions
draft: false
module: The Hot Big Bang
moduleNumber: 12
lessonNumber: 7
order: 1207
summary: >
  Five independent lines of evidence converge on a universe whose energy budget is
  dominated by dark energy and dark matter, with ordinary baryons a small remainder.
  The candidate particles for dark matter range from WIMPs to axions to sterile
  neutrinos, each with its own detection strategy. The concordance model fits the
  data with six parameters but leaves the nature of dark energy, the Hubble tension,
  small-scale structure, and the matter-antimatter asymmetry unexplained.
topics: [The Hot Big Bang]
sources:
  - book: Ryden
    ref: "Ch. 7 — Dark Matter; Ch. 13"
  - book: PDG
    ref: "Review of Particle Physics — Dark Matter and Cosmological Parameters"
  - book: Planck 2018
    ref: "Planck 2018 results VI. Cosmological parameters, A&A 641, A6"
---

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.

$$
% caption: Independent probes on galactic to cosmological scales converge on the
% same conclusion: the gravitating mass exceeds the baryonic mass by roughly a
% factor of five to ten.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
% central conclusion
\node[draw=acc, fill=acc!12, minimum width=2.4cm, minimum height=1.0cm, align=center] (dm) at (5.0,2.0) {dark matter\\ dominates mass};
% five probes around
\node[draw=black, align=center, minimum height=0.7cm] (rot) at (0.9,3.6) {rotation\\ curves};
\node[draw=black, align=center, minimum height=0.7cm] (cl) at (0.9,0.5) {clusters};
\node[draw=black, align=center, minimum height=0.7cm] (ls) at (5.0,4.1) {lensing};
\node[draw=black, align=center, minimum height=0.7cm] (cmb) at (9.1,3.6) {CMB\\ third peak};
\node[draw=black, align=center, minimum height=0.7cm] (st) at (9.1,0.5) {structure\\ growth};
\draw[->] (rot) -- (dm);
\draw[->] (cl) -- (dm);
\draw[->] (ls) -- (dm);
\draw[->] (cmb) -- (dm);
\draw[->] (st) -- (dm);
\end{tikzpicture}
$$

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 $\Gamma = n\langle\sigma_A v\rangle$ falls below $H$, the comoving number
freezes at a relic abundance that scales inversely with the annihilation cross
section,

$$
\Omega_{\text{dm}}h^2 \approx \frac{3 \times 10^{-27}\ \text{cm}^3\,\text{s}^{-1}}
{\langle\sigma_A v\rangle} .
$$

A weak-scale cross section, $\langle\sigma_A v\rangle \sim 10^{-26}\
\text{cm}^3\,\text{s}^{-1}$, 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.

$$
% caption: The same interaction vertex read three ways. Direct detection observes
% scattering off a nucleus, indirect detection observes annihilation products, and
% colliders attempt to produce the particles.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
% central vertex
\fill[acc] (5.0,2.2) circle (3pt);
\node[acc, anchor=south] at (5.0,2.4) {interaction};
% direct: DM in, DM out, nucleus recoils
\node[draw=black, align=center] (dir) at (1.4,3.4) {direct:\\ scattering};
\node[draw=black, align=center] (ind) at (1.4,1.0) {indirect:\\ annihilation};
\node[draw=black, align=center] (col) at (8.6,2.2) {collider:\\ production};
\draw[<->] (dir) -- (5.0,2.2);
\draw[<->] (ind) -- (5.0,2.2);
\draw[<->] (col) -- (5.0,2.2);
\node[black, anchor=north] at (5.0,1.9) {dark matter and Standard Model};
\end{tikzpicture}
$$

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

$$
\Omega_\Lambda \approx 0.69,
\qquad \Omega_{\text{dm}} \approx 0.26,
\qquad \Omega_b \approx 0.05,
$$

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.

$$
% caption: The present cosmic energy budget: dark energy about 69 percent, dark
% matter about 26 percent, and baryonic matter about 5 percent, with radiation
% negligible.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
% pie chart: dark energy 69% (248 deg), dark matter 26% (94 deg), baryons 5% (18 deg)
% start at 90 deg, go clockwise
\filldraw[fill=acc!12, draw=acc, very thick] (0,0) -- (90:2.6) arc (90:-158:2.6) -- cycle;
\draw[very thick] (0,0) -- (-158:2.6) arc (-158:-252:2.6) -- cycle;
\draw[very thick] (0,0) -- (-252:2.6) arc (-252:-270:2.6) -- cycle;
% labels
\node[black!75, anchor=west] at (3.0,1.4) {dark energy: 69 percent};
\node[black!75, anchor=west] at (3.0,0.4) {dark matter: 26 percent};
\node[black!75, anchor=west] at (3.0,-0.6) {baryons: 5 percent};
\draw[acc] (2.9,1.4) -- (2.5,1.4);
\draw[black] (2.9,0.4) -- (2.5,0.4);
\draw[black] (2.9,-0.6) -- (2.5,-0.6);
\end{tikzpicture}
$$

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.

$$
% caption: Supernovae, the CMB, and baryon acoustic oscillations each constrain a
% band in the matter density versus dark-energy density plane; the three bands
% intersect at a single flat, accelerating cosmology.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
\draw[->, black] (0,0) -- (6.4,0) node[right, black!70] {matter density};
\draw[->, black] (0,0) -- (0,5.2) node[above, black!70] {dark-energy density};
% flat line: Omega_m + Omega_L = 1
\draw[black, dashed] (0.4,4.6) -- (5.0,0.0);
\node[black, anchor=west] at (0.4,0.55) {zero curvature};
% SN band (upper-left to lower-right diagonal)
\draw[black] (0.6,4.4) -- (1.2,4.4) -- (4.0,0.4) -- (3.4,0.4) -- cycle;
\node[anchor=south] at (1.0,4.4) {SNe};
% CMB band (narrow diagonal along flatness)
\draw[black] (0.7,4.3) -- (1.0,4.6) -- (4.8,0.5) -- (4.5,0.2) -- cycle;
\node[anchor=west] at (4.8,0.7) {CMB};
% BAO band (steeper)
\draw[black] (2.2,0.3) -- (2.7,0.3) -- (3.6,4.8) -- (3.1,4.8) -- cycle;
\node[anchor=south] at (3.4,4.8) {BAO};
% intersection
\fill[acc] (2.9,2.1) circle (2.4pt);
\node[acc, anchor=west] at (3.0,2.3) {concordance};
\end{tikzpicture}
$$

## 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, $w \neq -1$) is unsettled;
  current data are consistent with $w = -1$ to about ten percent.

> **Worked example.** The observed dark-energy density is
> $\varepsilon_\Lambda \approx 0.69\,\varepsilon_{\text{crit}} \approx 6 \times
> 10^{-10}\ \text{J m}^{-3}$. A naive quantum-field estimate sums the zero-point
> energies of all modes up to the Planck scale, giving a vacuum density of order
> $\varepsilon_{\text{Pl}} \sim (M_{\text{Pl}}c^2)^4/(\hbar c)^3 \approx 10^{111}\
> \text{J m}^{-3}$. The ratio is
> $$
> \frac{\varepsilon_{\text{Pl}}}{\varepsilon_\Lambda} \sim 10^{120},
> $$
> the largest discrepancy between theory and observation in physics. Even cutting
> the sum off at the electroweak scale leaves a mismatch of $10^{55}$. No accepted
> mechanism explains why the vacuum energy is so small yet nonzero.
- **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.

$$
% caption: The Hubble tension. The early-universe value inferred from the CMB
% assuming the concordance model sits near 67, while the local distance ladder
% gives about 73; the error bars do not overlap.
\begin{tikzpicture}[scale=1.0, font=\footnotesize]
\definecolor{acc}{HTML}{4A6FA5}
\draw[->, black] (0,0) -- (9.4,0) node[right, black!70] {Hubble constant};
% axis ticks
\foreach \x/\lab in {1.5/65,4.0/68,6.5/71,9.0/74}
  \draw[black] (\x,0.08) -- (\x,-0.08) node[below, black] {\lab};
% early-universe measurement near 67.4 -> x approx 3.2
\fill[acc] (3.2,2.6) circle (2.4pt);
\draw[acc, very thick] (2.8,2.6) -- (3.6,2.6);
\node[acc, anchor=south] at (3.2,2.75) {early universe (CMB)};
% late-universe measurement near 73 -> x approx 7.7
\fill[black!70] (7.7,1.4) circle (2.4pt);
\draw[black!70, very thick] (7.3,1.4) -- (8.1,1.4);
\node[black!70, anchor=south] at (7.7,1.55) {local ladder};
% gap bracket
\draw[black, densely dotted] (3.2,2.6) -- (3.2,0.5);
\draw[black, densely dotted] (7.7,1.4) -- (7.7,0.5);
\draw[<->, black] (3.2,0.6) -- (7.7,0.6);
\node[black, anchor=north] at (5.45,0.55) {the tension};
\end{tikzpicture}
$$

The hot Big Bang model quantitatively accounts for the expansion, the light
elements from [nucleosynthesis](/astrophysics-cosmology/the-hot-big-bang/big-bang-nucleosynthesis),
the [microwave background](/astrophysics-cosmology/the-hot-big-bang/recombination-and-the-cosmic-microwave-background)
and its [acoustic peaks](/astrophysics-cosmology/the-hot-big-bang/cmb-anisotropies-and-cosmological-parameters),
and the [growth of structure](/astrophysics-cosmology/the-hot-big-bang/structure-formation-and-the-growth-of-perturbations)
from the perturbations that [inflation](/astrophysics-cosmology/the-hot-big-bang/cosmic-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.[^planck-open]

[^planck-open]: Planck Collaboration, Planck 2018 results VI, and the Particle Data Group Review of Particle Physics (Dark Matter, Cosmological Parameters) — the concordance energy budget, the dark-matter candidates and detection strategies, and the standing tensions of $\Lambda$CDM. https://arxiv.org/abs/1807.06209 ; https://pdg.lbl.gov