The hidden components of the universe — evidence, properties and the composition of the cosmos
AQA A-Level Physics — Astrophysics
🌌Explain what dark matter is and why it is so named
🔭Describe evidence for dark matter: galaxy rotation curves and gravitational lensing
⚡Explain dark energy and the accelerating expansion of the universe
📊State the approximate composition of the universe by energy density
💥Link dark energy to Type Ia supernova observations
🌐Discuss the implications for the ultimate fate of the universe
Dark Matter
Dark matter: Matter that does not interact with electromagnetic radiation (does not emit, absorb or reflect light) but has gravitational effects that are clearly detectable. It makes up about 27% of the total energy content of the universe.
Evidence for dark matter:
Galaxy rotation curves: The orbital speed of stars in a galaxy should decrease with distance from the centre (as for planets in the solar system, where v ∝ 1/√r beyond the mass). Instead, rotation curves are flat — stars at the outer edges orbit just as fast as those near the centre. This implies far more mass exists beyond the visible disk than can be seen. This unseen mass is dark matter distributed in a halo around the galaxy.
Gravitational lensing: Light from distant objects is bent by massive objects (Einstein's general relativity). When lensing is stronger than the visible mass can account for, additional invisible mass (dark matter) must be present. The Bullet Cluster shows dark matter separated from ordinary hot gas during a collision, providing direct evidence for dark matter as a distinct component.
Galaxy clusters: The velocity dispersion of galaxies in clusters (originally observed by Zwicky in 1933) implies far more gravitational mass than visible stars provide — the "missing mass" is dark matter.
Dark matter interacts only via gravity (and possibly the weak force — hence "Weakly Interacting Massive Particles", WIMPs, are the leading candidate). It does not interact electromagnetically, making it invisible. Its exact nature is one of the biggest unsolved problems in physics.
Dark Energy
Dark energy: A form of energy with negative pressure that permeates all of space and drives the accelerating expansion of the universe. It makes up approximately 68% of the total energy content of the universe.
Evidence for dark energy — accelerating expansion:
Type Ia supernovae are "standard candles" — they have a known intrinsic luminosity, so their distance can be measured from their apparent brightness.
In 1998, Riess, Perlmutter and Schmidt found that distant Type Ia supernovae were dimmer than expected — they were further away than a decelerating (or constant) expansion model predicted.
This implies the expansion of the universe is accelerating — the rate of expansion is increasing over time.
A new component with repulsive gravitational effect is required: dark energy. It is often modelled as the cosmological constant Λ (Einstein's "greatest blunder" that turned out to be real).
The nature of dark energy is completely unknown. It may be a property of space itself (vacuum energy), a new field (quintessence), or a sign that general relativity needs modifying at cosmological scales. Like dark matter, it is a profound mystery in modern physics.
Composition of the Universe
The current best measurements (from CMBR data — Planck satellite) give the following breakdown of the total energy density of the universe:
Component
Approximate %
Nature
Ordinary (baryonic) matter
~5%
Stars, gas, planets, you — anything made of atoms
Dark matter
~27%
Unknown particles; detected only gravitationally
Dark energy
~68%
Unknown; drives accelerating expansion
We can directly observe or study only ~5% of the universe's content. The remaining ~95% (dark matter + dark energy) is completely unknown in nature — one of the most humbling facts of modern cosmology.
These percentages are by energy density. Dark matter and dark energy cannot be directly detected in a laboratory on Earth with current technology — all evidence is indirect (gravitational effects, cosmic observations).
Fate of the Universe
The ultimate fate of the universe depends on the properties of dark energy:
If dark energy is constant (Λ): The universe expands forever, accelerating. Galaxies recede faster than light (outside the Hubble sphere) — eventually isolated island universes, then heat death (maximum entropy, no energy available to do work).
If dark energy strengthens over time: The expansion accelerates dramatically — the "Big Rip" (galaxies, then stars, then atoms themselves are torn apart).
If dark energy weakens or reverses: Expansion decelerates and might reverse — the "Big Crunch" (universe collapses back to a singularity).
Current data favour an eternally expanding universe with constant dark energy. However, the uncertainties are large enough that other scenarios cannot be ruled out. The fate of the universe is intimately tied to the still-unknown nature of dark energy.
Stars at the edge of a galaxy (radius 30 kpc from centre) orbit at 220 km s⁻¹ — the same speed as stars 5 kpc from the centre. (a) Estimate the total mass enclosed within 30 kpc. (b) The visible mass (stars) accounts for only 5% of this. What fraction is dark matter? (1 pc = 3.086 × 10¹⁶ m; G = 6.67 × 10⁻¹¹ N m² kg⁻²)
1Orbital radius r = 30 kpc = 30 × 10³ × 3.086 × 10¹⁶ = 9.26 × 10²⁰ m
2Gravitational force = centripetal force: GMm/r² = mv²/r → M = v²r/G
4Visible mass = 5% of 6.72×10⁴¹ = 3.36×10⁴⁰ kg. Dark matter fraction = 95%
Total enclosed mass ≈ 6.7 × 10⁴¹ kg; dark matter ≈ 95% of this (≈ 6.4 × 10⁴¹ kg)
A distant Type Ia supernova has an observed peak apparent magnitude m = 24.2. Its intrinsic luminosity corresponds to absolute magnitude M = −19.3. Calculate its distance modulus and use it to find the distance in Mpc (distance modulus = m − M = 5 log₁₀(d/10 pc)).
State two differences between dark matter and dark energy.
1Dark matter: has gravitational attraction (clusters with ordinary matter and in galaxy halos); causes structure formation; makes up ~27% of universe's energy content.
2Dark energy: causes gravitational repulsion (negative pressure) driving accelerating expansion; is uniform throughout space (does not cluster); makes up ~68% of universe's energy content.
Dark matter: gravitationally attractive, clusters in galaxy halos, ~27%. Dark energy: repulsive (drives acceleration), spatially uniform, ~68%.
Explain how gravitational lensing provides evidence for dark matter, without needing to detect the dark matter directly.
1General relativity predicts that mass bends the path of light. A massive object between a distant source and the observer acts as a "gravitational lens," distorting or multiplying the image of the background source.
2The amount of lensing (degree of image distortion, arc length, number of images) depends on the total mass along the line of sight — both visible and invisible.
3When the observed lensing is stronger than can be explained by the visible matter (stars, gas), additional invisible mass (dark matter) must be present. This works even though dark matter emits no light — its gravity still bends light.
Gravitational lensing bends light in proportion to total mass. When observed lensing exceeds what visible matter can explain, dark matter is required — detected through its gravity, not its light.
1. Approximately what percentage of the total energy content of the universe is ordinary (baryonic) matter?
The universe is ~5% ordinary matter, ~27% dark matter, ~68% dark energy. We can see and study only this 5%.
2. Galaxy rotation curves show that stars at large distances from the galactic centre orbit at approximately constant speed. What does this imply?
For a point mass or most mass concentrated centrally, v ∝ 1/√r at large r. Flat rotation curves require M(r) ∝ r — mass increasing linearly with radius — implying a spherical dark matter halo extending well beyond the visible galaxy.
3. What observation in 1998 provided the main evidence for dark energy (accelerating expansion)?
Type Ia supernovae have known intrinsic brightness. Those at high redshift were dimmer than expected — further away than models predicted — implying the expansion is accelerating. Riess and Perlmutter won the 2011 Nobel Prize for this discovery.
4. Dark matter differs from ordinary matter in that it:
Dark matter has positive mass and interacts gravitationally (attractively), but does not interact electromagnetically. This is why it is "dark" — it cannot be seen with any telescope operating at any wavelength of electromagnetic radiation.
5. The universe is approximately 5% ordinary matter and 27% dark matter. What percentage is dark energy?
1. The Bullet Cluster (1E 0657-558) consists of two galaxy clusters that have passed through each other. X-ray observations show the hot gas (ordinary matter) has been slowed by electromagnetic drag between the two clusters and lags behind. Gravitational lensing shows most of the mass is in two distinct clumps that have passed through and are ahead of the gas. Explain how this provides "smoking gun" evidence for dark matter.
In the Bullet Cluster collision: (1) The hot gas (visible ordinary matter — most of the baryonic mass) is detected by X-ray emission. It has been slowed and distorted by electromagnetic interactions (ram pressure) between the two cluster's gas clouds — it lags behind. (2) Gravitational lensing maps the total mass distribution. The lensing shows two large mass concentrations that have passed through each other, well ahead of the X-ray gas. (3) The mass detected by lensing cannot be the gas — the gas is in a different location. The lensing mass must be in a component that did not interact with the gas and passed through freely: dark matter. Dark matter (like the galaxies themselves, which are mostly space) passed through the collision without slowing — it interacts only gravitationally, not electromagnetically. This is the most direct observational evidence that dark matter is a separate, non-baryonic component rather than a modification of gravity (MOND alternatives struggle to explain the Bullet Cluster).
2. If dark energy has constant energy density (cosmological constant Λ) but ordinary and dark matter density decreases as the universe expands, explain why dark energy came to dominate only recently (at z ≈ 0.3, about 4 billion years ago) rather than from the beginning.
The energy density of matter (ordinary + dark) scales as ρ_matter ∝ 1/V ∝ 1/a³ (where a is the scale factor — it dilutes as the universe expands, volume ∝ a³). Radiation energy density scales as ρ_radiation ∝ 1/a⁴ (additional factor because wavelength also stretches). Dark energy density ρ_Λ is constant — it is a property of space itself, so as new space is created by expansion, the total dark energy increases at the same rate. In the very early universe, radiation dominated (ρ_radiation >> ρ_Λ). As the universe expanded, radiation diluted rapidly (∝ 1/a⁴) and matter took over (matter-dominated era from ~50,000 years to ~9.8 billion years). Matter diluted more slowly (∝ 1/a³), but still diluted. Eventually, around 4 billion years ago (a ≈ 0.77, z ≈ 0.3), ρ_matter fell below ρ_Λ and dark energy began to dominate — triggering the transition from decelerating to accelerating expansion. Today the universe is dark-energy-dominated (68%), but it was not always so. The "coincidence problem" — why do we happen to live at the epoch when ρ_matter ≈ ρ_Λ — is itself an unsolved puzzle.
3. Describe three proposed candidates for dark matter and one reason why each has not yet been confirmed.
(1) WIMPs (Weakly Interacting Massive Particles) — hypothetical particles with mass ~10–1000 GeV that interact via gravity and the weak force. They arise naturally in supersymmetric extensions of the Standard Model (e.g. neutralino). Not yet confirmed: decades of direct detection experiments (LUX, XENON1T, PandaX) have found no WIMP signal, ruling out large swathes of the predicted parameter space. LHC has also found no supersymmetric particles. (2) Axions — very light particles (mass ~10⁻⁵ eV) originally proposed to solve the strong CP problem in QCD. They could be produced in large quantities in the early universe. Not yet confirmed: axion detection requires very sensitive resonant cavity experiments (ADMX, HAYSTAC). No confirmed signal yet, though the parameter space is large and searches are ongoing. (3) Primordial black holes (PBHs) — black holes formed in the early universe (not from stellar collapse) before nucleosynthesis. They could provide dark matter without new particle physics. Not yet confirmed: microlensing surveys (MACHO, EROS, Subaru HSC) have ruled out PBHs as the dominant component across most mass ranges, except perhaps around 10⁻¹²–10⁻¹¹ M_sun (asteroid mass). Recent LIGO detections of black hole mergers renewed interest but the observed masses don't match the expected PBH mass range cleanly.
Objective: Use observational data to plot rotation curves and infer the presence of dark matter.
Background
Real rotation curves are obtained from radio observations of the 21-cm emission line of neutral hydrogen in the disk of spiral galaxies. By measuring the Doppler shift of this line at different positions across the galaxy, astronomers can map the orbital speed at different radii.
Method
Use provided data for a spiral galaxy (e.g. Milky Way or M31): orbital speed v (km s⁻¹) vs radius r (kpc).
Plot the observed rotation curve (v vs r).
Calculate the expected rotation curve if all mass is in the visible disk: beyond the disk, v ∝ 1/√r. Plot this expected curve.
Compare observed and expected curves. The difference indicates the presence of dark matter.
Estimate the enclosed dark matter mass at a given radius using M = v²r/G.
Sample Data (Milky Way)
r / kpc
v_observed / km s⁻¹
v_expected (without DM) / km s⁻¹
5
220
220
10
220
155
20
215
110
30
218
90
40
210
78
The flat observed curve vs the predicted decline provides direct evidence for a dark matter halo.
Discussion
Why is 21-cm radio emission useful for tracing gas at the galaxy's outer edges (beyond the visible stars)?
What assumptions are made when deriving M = v²r/G for circular orbits?
How would the rotation curve change if dark matter were concentrated at the centre rather than distributed in a halo?