(d) Cosmology
- Syllabus
- 2024
- Topic
- —
- Level
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Learning objectives
813P Big Bang theoryDescribe the past evolution of the universe and the main arguments in favour of the Big Bang theory814P Big Bang evidenceDescribe evidence that supports the Big Bang theory (red-shift and cosmic microwave background - CMB - radiation)815P Moving wave sourcesDescribe that if a wave source is moving relative to an observer, there will be a change in the observed frequency and wavelength816P Red-shift equationUse change in wavelength ÷ reference wavelength = galaxy velocity ÷ speed of light: Δλ/λ₀ = v/c, where Δλ = λ − λ₀.817P Galaxy red-shiftDescribe the red-shift in light received from galaxies at different distances away from the Earth818P Expansion of the universeExplain why the red-shift of galaxies provides evidence for the expansion of the universe
Describe the universe from the Big Bang to today
The Big Bang theory describes the universe as beginning in an extremely hot, dense state. Since then, the universe has expanded and cooled.
Past-to-present sequence: an early hot, dense universe → continuing expansion → increasing size and falling average temperature → the cooler, much larger universe observed today. The theory describes the expansion of the universe itself, not matter exploding from one location into an already existing universe.
The main observational arguments are that light from distant galaxies is red-shifted, showing large-scale expansion, and that cosmic microwave background radiation is detected throughout space as cooled radiation from the hot early universe. These independent observations match predictions of the theory.
A scientific theory is supported by observations rather than proved by its name. The Big Bang model does not say that the universe has stayed the same size or temperature; expansion and cooling are central to its past evolution.
Explain the two main lines of Big Bang evidence
Two observations support the Big Bang theory: the cosmological red-shift of galaxies and cosmic microwave background radiation (CMBR). Each links the present universe to an earlier, hotter and denser state.
| Observation | What is measured | Why it supports the Big Bang |
|---|---|---|
| cosmological red-shift | spectral lines from most distant galaxies are shifted to longer wavelengths; more distant galaxies generally have greater red-shift | galaxies are receding and the universe is expanding; reversing that expansion places matter closer together in the past |
| CMBR | faint microwave radiation arrives from all directions and is nearly uniform | it is consistent with radiation from a once-hot universe whose wavelength increased as the universe expanded and cooled |
The evidence is stronger as a pair: red-shift describes continuing large-scale expansion, while CMBR is a surviving signal of the universe's hotter past. Both are consequences expected from the same expanding-universe history.
Naming red-shift or CMBR is not the complete explanation. The observation must be connected to expansion, earlier closeness or higher past temperature. Red-shift is evidence from galaxies; CMBR is background radiation, not ordinary light from one nearby star.
Relate source motion to observed wavelength and frequency
When a wave source moves relative to an observer, the observer detects a different wavelength and frequency from those emitted by a stationary source. This is the Doppler effect.
| Relative motion | Observed wavelength | Observed frequency |
|---|---|---|
| source moving towards observer | shorter | higher |
| source moving away from observer | longer | lower |
A source moving towards the observer emits successive wavefronts from positions closer to the observer, so the wavefronts arrive more closely spaced. Moving away spreads their arrival positions farther apart. For visible light, a shift to longer wavelength towards the red end of the spectrum is called red-shift.
The change depends on relative motion along the line between source and observer, not simply on the source being far away. The observed wavelength and frequency change together in opposite directions; a longer wavelength means a lower frequency, not a lower wave speed in vacuum.
Calculate cosmological red-shift and galaxy velocity
The fractional change in wavelength equals the galaxy's recession speed as a fraction of the speed of light.
\frac{\Delta\lambda}{\lambda_0}=\frac{v}{c},\qquad \Delta\lambda=\lambda-\lambda_0
λ0 is the reference wavelength measured for the same spectral line at rest, λ is the wavelength observed from the galaxy, Δλ is the change, v is galaxy velocity and c is the speed of light. For red-shift, λ>λ0, so Δλ is positive. Use the same units for both wavelengths and the same speed units for v and c.
Example: a hydrogen line has λ0=605 nm and is observed at λ=683 nm. Δλ=683−605=78 nm, so v=3.0×108×(78/605)=3.9×107 m/s.
Calculate the wavelength change before forming the ratio; do not use the observed wavelength in place of λ0. Wavelength units cancel only when they match. If the question asks for observed wavelength after finding Δλ, use λ=λ0+Δλ for a red-shift.
Compare galaxy red-shift at different distances
Light from more distant galaxies generally shows a greater cosmological red-shift than light from nearer galaxies.
| Galaxy comparison | Spectral-line shift | Observed wavelength | Inferred recession speed |
|---|---|---|---|
| nearer galaxy | smaller red-shift | less increase above the reference wavelength | lower |
| farther galaxy | greater red-shift | greater increase above the reference wavelength | higher |
For the same reference spectral line, if galaxy Q is twice as far away as galaxy P and follows the observed distance–speed relationship, Q recedes about twice as fast and has about twice the wavelength change. Its detected line is therefore shifted farther towards longer wavelengths.
Compare the same identifiable spectral line with its laboratory reference wavelength. A greater observed wavelength is interpreted as greater red-shift only after this reference comparison; distance does not change which element emitted the line.
Use red-shift as evidence that the universe expands
Cosmological red-shift shows that galaxies are separating on a large scale, which is evidence that the universe is expanding.
Reasoning chain: most distant galaxies show red-shift → their light has longer wavelength → they are moving away → more distant galaxies generally show greater red-shift and higher recession speed → distances between galaxies are increasing as the universe expands.
If this expansion is traced backwards in time, galaxies and matter were closer together. Continuing the backward model leads to the hot, dense early state described by the Big Bang theory, so the distance–red-shift pattern supports both present expansion and the universe's past evolution.
One red-shifted galaxy alone would show only that one source is receding. The evidence for universal expansion is the systematic pattern across many galaxies, especially the increase of recession speed with distance. Red-shift is an observation; expansion is the conclusion drawn from that pattern.