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Cosmology asks the biggest question on the paper, how the universe began, but the marks go to precise small steps: a redshift calculation, the unit conversion in a Hubble’s-law question, and an evidence argument set out clearly. Expect 2–4 mark calculations and a 6-mark “evaluate the evidence” question.
By the end you’ll be able to
Use z = Δλ/λ ≈ v/c and Δf/f ≈ v/c for sources moving much slower than light
Apply Hubble’s law v = H₀d and estimate the age of the universe as 1/H₀, handling unit conversions (km s⁻¹ Mpc⁻¹ to s⁻¹)
Explain the evidence for the Big Bang: galactic redshift, cosmic microwave background radiation, relative abundance of hydrogen and helium
Describe evidence for dark matter (galaxy rotation curves) and dark energy (type Ia supernovae)
Describe quasars and the radial-velocity and transit methods for exoplanets (AQA option)
What the exam asks
Redshift: z=Δλ/λ≈v/c for galaxies, binary stars and exoplanet “wobbles”.
Hubble’s law: v=H0d, H0 as the gradient of a graph, and the age estimate with correct units.
Evidence for the Big Bang (redshift, the CMB, the hydrogen and helium abundances), for dark matter (rotation curves) and for dark energy (type Ia supernovae).
Board extras: quasars and exoplanets (AQA), the cosmological principle and the timeline of the universe (OCR A), and radial velocities and critical density (Eduqas, WJEC).
Core ideas
Redshift
Light from a receding source arrives with a longer wavelength (redshift), and light from an approaching source with a shorter one (blueshift). For v≪c:
z=λ
vii.Check your understanding
3 questions on cosmology: redshift, Hubble’s law and the Big Bang. Every option is explained once you answer.
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PromptCard 1 of 3
Give the Doppler redshift equation, and say what λ and v mean.
1/H0
=
−v/c
v=Hd
H=65km s−1Mpc−1
v
z>0
Edexcel 9PH0 and IAL: z=Δλ/λ≈Δf/f≈v/c, v=H0d, 1/H0, and the debate over the age and fate of the universe.
OCR A (5.5.3): the cosmological principle, the Doppler, Hubble and t=H0−1 equations (all on the data sheet), the CMB, the evolution of the universe, and dark matter and dark energy.
OCR B (“Our place in the universe”): redshift, Hubble’s law and the evidence for a hot Big Bang.
Cambridge 9702 (25.3, Paper 4): redshift (given), and v≈H0d, which you must recall and use in SI units only.
Eduqas (C2) and WJEC (Unit 4): Δλ/λ=v/c, radial velocities in double-star and star–planet systems, rotation curves, v=H0D, 1/H0 and ρc=3H02/8πG.
CCEA (AS 2): redshift, Hubble’s law and the age of the universe.
Δ
λ
≈
fΔf≈
cv
Here λ is the laboratory (rest) wavelength, and v is the radial velocity, the component along the line of sight. Astronomers identify a known pattern of absorption lines and measure how far the whole pattern has moved. Every line shifts by the same fraction of its wavelength.
Binary stars and exoplanets
Two stars, or a star and a planet, orbit their common centre of mass. Seen edge-on, each star alternately approaches and recedes, so its lines oscillate about the rest wavelength. The period of the oscillation is the orbital period T. The maximum shift gives the orbital speed v, and for a circular orbit r=vT/2π. Eduqas and WJEC then find the masses from m1r1=m2r2 and Newton’s law of gravitation.
Exoplanets (AQA) are hard to image directly. They are extremely faint and so close to their star in angle that its glare swamps them.
Method
Observed
Favours
Needs
Radial velocity
periodic Doppler shift of the star’s lines
massive planets close to the star
orbit not face-on
Transit
periodic, flat-bottomed dip in brightness
large planets close to the star
orbit almost edge-on
The fractional dip during a transit is about (Rplanet/Rstar)2, the ratio of the disc areas.
Hubble’s law and the age of the universe
v=H0d
H0 is the gradient of a graph of v against d. Measurements range from about 67 to 73 km s−1Mpc−1, and different methods still disagree. The AQA booklet uses 65.
Interpretation: space itself is expanding, and the expansion stretches light’s wavelength as it travels. There is no centre, because observers in every galaxy see the same pattern. OCR A’s cosmological principle says that on large scales the universe is homogeneous and isotropic, and the laws of physics are the same everywhere.
Age: if the expansion rate has been constant, every galaxy took t=d/v=1/H0 to reach its present distance. With 1Mpc=3.08×1022 m:
The universe began about 14 billion years ago in an extremely hot, dense state, and it has been expanding and cooling ever since.
Redshift: the galaxies are moving apart, so they were once much closer together.
The CMB: microwave radiation arrives almost equally from every direction, with a black-body spectrum at 2.7 K (peak wavelength about 1 mm). About 380 000 years after the Big Bang, the universe had cooled to about 3000 K. Atoms formed, the universe became transparent, and this radiation was released. Expansion has since stretched its wavelength by a factor of about 1100. A steady-state universe cannot explain it.
Hydrogen and helium: fusion in the first few minutes gives about 75% hydrogen and 25% helium by mass, which matches the oldest stars and gas clouds.
Dark matter and dark energy
Rotation curves: if a galaxy’s mass were where its stars are, orbital speeds far out would fall as v=GM/r. Instead they stay roughly constant, which points to a large halo of unseen dark matter.
Dark energy: distant type Ia supernovae look fainter, so they are further away, than steady expansion predicts. The expansion is accelerating. The current estimates are about 5% ordinary matter, 27% dark matter and 68% dark energy.
Critical density (Eduqas, WJEC): for a galaxy at the edge of a uniform sphere, set 21mv2=GMm/r, with M=34πr3ρ and v=H0r. This gives ρc=3H02/8πG≈, about five hydrogen atoms per cubic metre. If the density is higher than this, gravity eventually halts the expansion (ignoring dark energy).
Quasars (AQA)
Quasars were first found as bright radio sources with star-like images and huge redshifts. They are thousands of megaparsecs away yet still look fairly bright, so their power is enormous: about 1039–1041 W, hundreds of times that of a whole galaxy. Their brightness changes within days, so the source is no bigger than the distance light travels in that time, which is about the size of the solar system. The explanation is matter falling into a supermassive black hole at the centre of a young galaxy.
Timeline (OCR A)
After the Big Bang
Event
about 10−6 s
quarks form protons and neutrons
first few minutes
helium nuclei form by fusion
about 380 000 years
atoms form and the CMB is released
about 200 million years
first stars, then galaxies
about 9 billion years
the Solar System forms
about 13.8 billion years
now
Worked examples
Exam technique
Write z=Δλ/λ with the rest wavelength, then v=zc.
Units: for d=v/H0, keep both in km s⁻¹ and the answer comes out in Mpc. Convert to s⁻¹ only for the age. Cambridge expects SI throughout.
Gradients: draw the line through the origin when theory says it passes through it, use a large triangle, and give H0 with its unit.
6-mark evidence answers: for each piece of evidence, give the observation, what the Big Bang predicts and why they match. For “evaluate”, add a limitation, such as the uncertainty in H0.
Common mistakes
Quick recap
z=Δλ/λ≈v/c, using the rest wavelength and the radial velocity.
v=H0d, and t≈1/H0≈14 billion years (1 Mpc =3.08×1022 m).
The evidence for the Big Bang is redshift, the 2.7 K CMB and about 75% H to 25% He by mass.
Flat rotation curves point to dark matter. Faint distant supernovae point to accelerating expansion.
Binary orbits: the period comes from the line oscillation, the speed from the maximum shift, and r=vT/2π.
Exoplanets are found by radial velocity or transit. Quasars are distant, enormously powerful and small.