HSC Exam Practice

Sample response. The Big Bang theory is the prevailing cosmological model stating that the universe began approximately 13.8 billion years ago from an extremely hot, dense state, and has been expanding and cooling ever since. Crucially, the Big Bang was NOT an explosion of matter into pre-existing empty space; it was the expansion of space itself. There was no “outside” space for matter to expand into — space, time, matter, and energy all originated at the Big Bang. The universe expanded from a singularity, with space itself stretching, not matter moving through a fixed background.

Marking notes. 1 mark for a correct definition of the Big Bang theory (hot, dense state ~13.8 Gyr ago, expanding and cooling). 1 mark for explicitly stating the Big Bang was an expansion OF space, not an explosion INTO space. 1 mark for explaining there was no pre-existing empty space (space, time, and energy all originated at the Big Bang).

Sample response. (1) The CMB has a perfect black-body spectrum at a temperature of 2.725 K — the most perfect thermal spectrum ever observed. (2) The CMB is extraordinarily uniform across the sky, the same temperature in all directions to about 1 part in 100,000. (3) The CMB has tiny temperature anisotropies of approximately ±30 μK, which represent the density fluctuations that seeded the formation of all large-scale cosmic structure (galaxies, clusters, voids).

Marking notes. 1 mark per correctly identified and described property. Accept: black-body spectrum at 2.725 K; uniformity/isotropy across the sky; tiny anisotropies (±30 μK or 1 in 100,000); microwave wavelength; fills the entire universe. Do not award marks for merely “thermal radiation” without temperature or spectrum detail.

Sample response. The relationship \(T \propto 1/a\) means that temperature is inversely proportional to the scale factor \(a\). In the early universe, \(a\) was much smaller than today (e.g. at recombination \(a \approx 1/1100\) of its current value), so the temperature was approximately 1100 times higher than the current 2.725 K, giving \(T \approx 3000\) K at recombination. Further back (e.g. \(a \approx 10^{-32}\)), temperatures reached \(10^{27}\) K during inflation. By convention, the present-day scale factor is set to \(a = 1\).

Marking notes. 1 mark for correctly stating \(T \propto 1/a\) means smaller \(a\) → higher T. 1 mark for a quantitative example (e.g. at recombination \(a \approx 1/1100\) so \(T \approx 3000\) K, or any valid numerical comparison). 1 mark for stating \(a = 1\) for the present-day universe.

Sample response. Doppler redshift: caused by relative motion of the source through space (the source and observer are moving relative to each other); dominates for nearby objects with significant peculiar velocities, e.g. nearby stars or galaxies in the Local Group. Gravitational redshift: caused by photons losing energy as they climb out of a gravitational potential well (longer wavelength = lower energy); dominates for compact massive objects, e.g. photons escaping from the surface of a white dwarf or neutron star. Cosmological redshift: caused by space itself expanding, stretching the wavelength of photons as they travel through it — the photon’s wavelength increases in proportion to the expansion of the universe; dominates for distant galaxies at cosmological distances. All three are described by \(z = \Delta\lambda/\lambda_{\text{rest}}\), but the physical cause differs.

Marking notes. 1 mark for correct cause of each type (3 marks total). 1 mark for correct context where each dominates (3 marks total).

Sample response. The student is incorrect because the recession of galaxies does not imply a centre. Using the balloon analogy: imagine dots (galaxies) on the surface of an inflating balloon (space). As the balloon expands, every dot moves away from every other dot — no dot is at the “centre” because the centre of the balloon is inside the balloon, not on the surface. Similarly, the universe expands in all directions uniformly; an observer in any galaxy would observe all other galaxies receding. The apparent recession of all galaxies from Earth does not make Earth central — every galaxy would observe the same pattern.

Marking notes. 1 mark for using the balloon analogy correctly (dots on surface = galaxies; inflation = expansion of space; no dot is at a special position). 1 mark for stating that any observer in any galaxy would see the same pattern of recession. 1 mark for explicit conclusion that the observation does not imply Earth is at the centre.

Sample response. Since peak wavelength \(\lambda_{\text{peak}} \propto 1/T\), and \(\lambda_{\text{obs}} = \lambda_{\text{emit}}(1+z)\): \[\frac{\lambda_{\text{obs}}}{\lambda_{\text{emit}}} = \frac{T_{\text{emit}}}{T_{\text{obs}}} = \frac{3000}{2.725} \approx 1100 = 1 + z\] Therefore \(z = 1100 - 1 \approx \mathbf{1099}\).

Marking notes. 1 mark for setting up the ratio \(\lambda_{\text{obs}}/\lambda_{\text{emit}} = T_{\text{emit}}/T_{\text{obs}}\) with correct reasoning. 1 mark for substituting values correctly (3000/2.725 ≈ 1100). 1 mark for the final answer z ≈ 1099 (accept 1098–1100).

Sample response (a). \(H_0 = v/d\): Galaxy A = 2100/30 = 70; Galaxy B = 5250/75 = 70; Galaxy C = 8640/120 = 72; Galaxy D = 14200/200 = 71; Galaxy E = 21300/300 = 71 km/s/Mpc. Mean H₀ = (70 + 70 + 72 + 71 + 71)/5 = 70.8 km/s/Mpc (accept 70–71 km/s/Mpc).

Marking notes (a). 1 mark for correctly calculating all five H₀ values. 1 mark for computing the mean correctly. 1 mark for the final mean answer in the range 70–72 km/s/Mpc.

Sample response (b). Galaxy D’s slightly higher H₀ (71 km/s/Mpc) may be due to a peculiar velocity — a local motion of the galaxy relative to the Hubble flow caused by gravitational interaction with neighbouring galaxies — which adds to or subtracts from the cosmological recession speed [1]. This does not invalidate Hubble’s law; the law describes the average large-scale behaviour of galaxies. Individual galaxies can have peculiar velocities of hundreds of km/s superimposed on the cosmological recession; these average out over large samples [1].

Sample response (c). v = H₀ × d = 70.8 × 500 ≈ 35,400 km/s (accept 35,000–35,500 km/s using mean H₀ from part a) [1 method, 1 answer].

Sample response. The Cosmic Microwave Background is among the most compelling evidence for the Big Bang theory. Its physical origin is the epoch of recombination, approximately 380,000 years after the Big Bang, when the universe had cooled to ~3000 K. Before this, the universe was an opaque plasma; photons scattered continuously off free electrons and could not travel freely. When the temperature dropped sufficiently, electrons combined with protons and helium nuclei to form neutral atoms (recombination). This made the universe transparent, and photons decoupled — travelling freely as thermal radiation. As the universe expanded over the subsequent ~13.8 billion years, these photons were cosmologically redshifted from the visible/infrared range to microwaves: using \(T \propto 1/a\), the factor of expansion since recombination is \(T_{\text{emit}}/T_{\text{obs}} = 3000/2.725 \approx 1100\), giving \(z \approx 1099\). [2 — physical origin including recombination, neutral atoms, and cosmological redshift calculation] The CMB has three key observational properties that support the Big Bang model: (1) a perfect black-body spectrum at 2.725 K, consistent with radiation that was in complete thermal equilibrium during the opaque plasma phase — no other known astrophysical process produces such a spectrum filling the entire universe; (2) extraordinary uniformity (±30 μK across the whole sky), consistent with the universe being nearly homogeneous at recombination as predicted by the Big Bang + inflation model; (3) tiny temperature anisotropies of ~1 part in 100,000, which match the predictions of primordial quantum fluctuations amplified by inflation and represent the seeds of all large-scale structure (galaxies, clusters, filaments). [2 — three properties with explanation of how each supports the model] One limitation of using the CMB alone is that it is indirect evidence — we observe the relic radiation, not the early universe itself. An alternative model would need to explain the black-body spectrum by some mechanism other than a hot dense phase, which is theoretically very difficult but not logically impossible. The evidence is strong but not from direct observation of the Big Bang itself. [1 — valid limitation] An additional independent line of evidence is Big Bang nucleosynthesis: the observed cosmic abundances of light elements (approximately 75% hydrogen, 25% helium by mass, with trace lithium and deuterium) match quantitative predictions made using the known physics of proton-neutron fusion at the temperatures and densities expected 3 minutes after the Big Bang. This agreement between theory and observation, using completely different physical processes from the CMB, greatly strengthens the Big Bang model. [1 — additional evidence with mechanism] Together, the CMB properties and nucleosynthesis abundances provide mutually reinforcing, independent evidence that the universe evolved from a hot, dense state consistent with the Big Bang theory. [1 — evaluative synthesis]

Marking criteria (7 marks). 1 = physical origin of CMB: recombination, neutral hydrogen forming, photon decoupling. 1 = cosmological redshift of CMB explained with reference to \(T \propto 1/a\) or z calculation. 1 = black-body spectrum described and linked to Big Bang (thermal equilibrium in plasma phase). 1 = uniformity and/or anisotropies described and linked to Big Bang predictions. 1 = reaches an evaluative judgement about the strength of the CMB as evidence (not just describes it). 1 = identifies one valid, specific limitation of CMB-only evidence. 1 = identifies and explains one additional independent line of evidence (nucleosynthesis abundances, Hubble expansion, large-scale structure, direct observation of galaxy evolution) with a specific physical mechanism or quantitative detail.