Physics • Year 12 • Module 8 • Lesson 1
The Big Bang Theory
Apply your understanding of cosmological redshift, the CMB, and Hubble’s law to real data, calculation scenarios and diagram critique.
1. Interpret CMB expansion data
The table below summarises key epochs in the universe’s history. 8 marks
| Epoch | Time after Big Bang | Temperature (K) | Key event | Universe transparent? |
|---|---|---|---|---|
| Planck era | ~10−43 s | ~1032 | Gravity separates from other forces | |
| Inflation | ~10−35 s | ~1027 | Exponential expansion | |
| Quark era end | ~10−6 s | ~1013 | Quarks combine into protons and neutrons | |
| Nucleosynthesis | ~3 min | ~109 | Proton & neutron fusion into nuclei | |
| Recombination | ~380,000 yr | ~3,000 | Electrons bind to nuclei; CMB released | |
| Present day | ~13.8 Gyr | 2.725 | Accelerating expansion continues |
1.1 Complete the “Universe transparent?” column for each epoch (Yes / No). 3 marks
1.2 Using the data in the table, describe the general relationship between time after the Big Bang and the temperature of the universe. 2 marks
1.3 Using T ∝ 1/a, calculate the factor by which the scale factor of the universe has increased since recombination (T = 3000 K) to today (T = 2.725 K). Show your working. 3 marks
2. Interpret a Hubble diagram — galaxy recession speeds
A student plots recession speed (km/s) against distance (Mpc) for six galaxies. The graph below shows the data. 8 marks
Figure 2. Recession speed vs distance for six galaxies. Illustrative data consistent with H₀ ≈ 70 km/s/Mpc.
2.1 Describe the relationship shown in the graph. 2 marks
2.2 Use the graph to estimate the Hubble constant H₀ (km/s/Mpc). Show your method. 2 marks
2.3 A galaxy is observed at a distance of 400 Mpc. Use your value of H₀ to predict its recession speed. 2 marks
2.4 A student argues: “Because all galaxies are moving away from us, Earth must be at the centre of the universe.” Identify the flaw in this reasoning and explain what the graph actually tells us about the structure of the universe. 2 marks
3. Compare three types of redshift
Complete the table to contrast the three types of redshift relevant to the HSC Physics course. 9 marks (1 per cell)
| Feature | Doppler redshift | Gravitational redshift | Cosmological redshift |
|---|---|---|---|
| Physical cause | |||
| Formula (same/different for all?) | |||
| Dominant for… |
4. Predict and justify — CMB wavelength scenario
When the CMB was emitted at recombination, photons had a peak wavelength corresponding to a blackbody at about 3000 K. Today, CMB photons are observed as microwaves with a peak wavelength corresponding to 2.725 K. The formula for cosmological redshift is: λobs = λemit(1 + z). 6 marks
4.1 Using T ∝ 1/λ for blackbody radiation, calculate the redshift z of the CMB. Show your working. 3 marks
4.2 If a CMB photon had a wavelength of 500 nm when emitted at recombination, calculate its wavelength today. Show your working. 2 marks
4.3 The calculated wavelength today would place the photon in which region of the electromagnetic spectrum? Is this consistent with the CMB being observed as microwave radiation? Justify. 1 mark
5. Diagram critique — what is wrong with this student’s Big Bang diagram?
A student drew the following description of the Big Bang: “The Big Bang was a massive explosion at a single point in space. Matter was thrown outward into empty space, and Earth is now at the centre because all galaxies are moving away from us.” There are three conceptual errors. Identify each error and write the correction. 6 marks (2 per error)
5.1 Error 1: What is wrong?
Correction:
5.2 Error 2: What is wrong?
Correction:
5.3 Error 3: What is wrong?
Correction:
Q1.1 — Transparency column
Planck era: No. Inflation: No. Quark era end: No. Nucleosynthesis: No. Recombination: Yes (universe becomes transparent at recombination). Present day: Yes. Award 1 mark for correctly filling in all epochs before recombination as “No” and recombination + present as “Yes” (3 marks: 1 for all pre-recombination No; 1 for recombination Yes; 1 for present Yes).
Q1.2 — Temperature-time relationship
As time after the Big Bang increases, the temperature of the universe decreases [1]. The relationship is not linear — temperature drops rapidly in the early universe and approaches 2.725 K today; as the universe expands, photons are redshifted to lower energies and the average temperature falls inversely with the scale factor [1].
Q1.3 — Scale factor calculation
T ∝ 1/a ⇒ anow/athen = Tthen/Tnow [1] = 3000 / 2.725 [1] ≈ 1100 [1]. The universe has expanded by a factor of approximately 1100 since recombination.
Q2.1 — Hubble diagram trend
There is a positive linear relationship between recession speed and distance [1]. Galaxies that are farther away are receding faster; the data points lie close to a straight line through the origin [1].
Q2.2 — Hubble constant from graph
Use two points on the best-fit line, e.g. (0, 0) and (100 Mpc, 7000 km/s): H₀ = Δv / Δd = 7000 / 100 = 70 km/s/Mpc [1 for method, 1 for answer in range 65–75 km/s/Mpc].
Q2.3 — Predicting recession speed
v = H₀ × d = 70 × 400 = 28,000 km/s [1 for method, 1 for answer]. Note: for very distant objects, the recession speed can exceed c; the simple Hubble formula is approximate.
Q2.4 — Flaw in reasoning (no centre)
The flaw is that the student assumes observations from Earth imply Earth is the centre [1]. The graph shows that recession speed is proportional to distance for all galaxies; an observer in any galaxy would observe the same pattern — the expansion of space is uniform and has no centre [1].
Q3 — Compare three types of redshift
Physical cause: Doppler: relative motion of source through space. Gravitational: photon climbing out of a gravitational field, losing energy. Cosmological: space itself expanding, stretching photon wavelengths en route.
Formula: All three are described by z = Δλ / λrest, but the physical interpretation of z differs. For cosmological redshift, v = cz is only an approximation (valid for z << 1).
Dominant for: Doppler: nearby objects with significant peculiar velocities (stars, nearby galaxies). Gravitational: compact massive objects (white dwarfs, neutron stars, black holes). Cosmological: distant galaxies; the dominant mechanism for large-scale structure.
Q4.1 — CMB redshift calculation
Since T ∝ 1/λ for blackbody radiation, λobs/λemit = Temit/Tobs [1] = 3000 / 2.725 ≈ 1100 [1]. Using λobs = λemit(1 + z): 1 + z = 1100, so z ≈ 1099 ≈ 1100 [1].
Q4.2 — Wavelength of CMB photon today
λobs = λemit(1 + z) = 500 × 10−9 m × 1100 [1] = 5.5 × 10−4 m = 0.55 mm [1].
Q4.3 — Region of spectrum
0.55 mm = 550 μm, which lies in the microwave region of the electromagnetic spectrum (microwaves span ~1 mm – 1 cm). This is fully consistent with the CMB being observed as microwave radiation [1].
Q5 — Diagram critique
5.1 Error 1 (the Big Bang as an explosion in space): The student incorrectly describes the Big Bang as “a massive explosion at a single point in space” [1]. Correction: The Big Bang was an expansion of space itself — there was no pre-existing space into which matter exploded. Space and time originated in the Big Bang; it occurred everywhere simultaneously [1].
5.2 Error 2 (matter thrown into empty space): The student implies there was pre-existing “empty space” for matter to expand into [1]. Correction: There was no pre-existing empty space; space itself expanded. Every point in the universe recedes from every other point as space stretches [1].
5.3 Error 3 (Earth at the centre because galaxies recede): The student claims Earth is at the centre of the universe [1]. Correction: The recession of galaxies in all directions does not indicate a centre; in a uniformly expanding universe, every observer in every galaxy sees all other galaxies receding. There is no privileged centre [1].