Physics • Year 12 • Module 8 • Lesson 2
Evidence for the Big Bang
Build HSC Band 5–6 extended-response technique on evaluating evidence, constructing scientific arguments, and integrating all three pillars of Big Bang evidence.
1. Data + scenario: reconciling lookback time with elemental abundances (Band 5–6)
9 marks Band 5–6
Scenario. A team of astronomers using the Australian SKA Pathfinder (ASKAP) radio telescope in Western Australia observes a distant quasar at $z = 6.5$. Using Wien’s law they also measure the CMB temperature in the direction of the quasar as exactly 2.725 K. Meanwhile, a nearby dwarf galaxy (halo population II stars, $z \approx 0.003$) shows helium mass fraction $Y = 0.249 \pm 0.003$ from spectroscopy of its H II regions. The table below summarises these measurements.
| Measurement | Value | Predicted by Big Bang model |
|---|---|---|
| CMB temperature | 2.725 K (isotropic) | 2.725 K (cooled relic radiation) |
| Helium mass fraction $Y$ | $0.249 \pm 0.003$ | $0.247 \pm 0.002$ (BBN calculation) |
| Deuterium-to-hydrogen ratio | $2.6 \times 10^{-5}$ (by number) | $2.5 \times 10^{-5}$ (BBN calculation) |
Illustrative data consistent with Planck Collaboration (2018) and Cooke et al. (2018).
Q1. Analyse and evaluate the data above to assess the strength of the evidence for the Big Bang model. In your response you must:
- Explain what the redshift $z = 6.5$ implies about the lookback time and the state of the universe when the quasar’s light was emitted.
- Assess whether the CMB measurement is consistent with the Big Bang prediction, and explain what it would mean if the CMB were found to be hotter in one direction.
- Evaluate whether the helium mass fraction $Y = 0.249 \pm 0.003$ supports the Big Bang nucleosynthesis (BBN) prediction, using the data in the table.
- Explain why the deuterium abundance is considered a sensitive “barometer” for Big Bang nucleosynthesis conditions.
- Identify one limitation of using this evidence to support the Big Bang model and suggest how it could be addressed.
2. Construct a scientific argument — defending the Big Bang against a sceptic (Band 5–6)
8 marks Band 5–6
Sceptic’s claim. “The Big Bang theory is just a theory — a guess. Galaxies could be moving through space (like a conventional explosion), not being carried by expanding space. The CMB could be from stars, and the helium could have been made in stars. None of these individually proves a Big Bang.”
Q2. Write a structured scientific response to the sceptic. Your response must:
- Clarify the scientific meaning of “theory” in the context of the Big Bang, distinguishing it from a guess or hypothesis.
- Counter the claim that galaxies are simply moving through space: use evidence and reasoning to show that cosmological redshift cannot be explained purely by the Doppler effect.
- Counter the claim that the CMB could come from stars, by explaining two specific features of the CMB that stellar radiation cannot replicate.
- Counter the claim about stellar helium production, using the deuterium abundance as supporting evidence.
- Conclude by explaining why the convergence of three independent lines of evidence strengthens the Big Bang model beyond what any single piece of evidence could establish.
Q1 — Sample Band 6 response (9 marks), annotated
Lookback time and $z = 6.5$ (1 mark): A redshift of $z = 6.5$ means that photon wavelengths have been stretched by a factor of $(1 + 6.5) = 7.5$ since the quasar emitted them. The light has been travelling for approximately 12.9 billion years (lookback time ~13 billion years), meaning we are observing the quasar when the universe was only about 900 million years old — less than 7% of its current age. This confirms that the universe has changed dramatically over time, consistent with Big Bang evolution rather than a steady state [1].
CMB consistency and implications of anisotropy (2 marks): The measured CMB temperature of 2.725 K matches the Big Bang model prediction precisely. The model predicts that relic radiation from recombination (~3000 K at $z \approx 1100$) should have been cooled by expansion by a factor of ~1100, giving $3000/1100 \approx 2.73$ K — consistent with measurement [1]. If the CMB were found to be systematically hotter in one direction, this would indicate a large-scale temperature anisotropy inconsistent with a universe that was nearly uniform at recombination. While tiny temperature fluctuations ($\Delta T/T \sim 10^{-5}$) are expected and observed as seeds of large-scale structure, a gross directional temperature difference would challenge the Big Bang model’s prediction of isotropy and might suggest the early universe had preferred directions — requiring a fundamental revision of cosmological models [1].
Helium mass fraction evaluation (2 marks): The measured helium fraction $Y = 0.249 \pm 0.003$ overlaps within the combined uncertainties with the BBN prediction of $0.247 \pm 0.002$ (overlap range 0.245–0.249). This agreement is statistically significant and supports the BBN prediction [1]. It is important that the measurement is made in a halo population (metal-poor stars) to minimise contamination from stellar nucleosynthesis; the result is consistent with primordial helium rather than stellar enrichment [1].
Deuterium as a barometer (2 marks): Deuterium (hydrogen-2) is extremely sensitive to the baryon density of the early universe: a higher baryon density would have fused more deuterium into helium-3 and helium-4, leaving a lower D/H ratio; a lower density would leave more deuterium. The measured D/H ratio therefore constrains the baryon density independently of any other measurement [1]. Furthermore, deuterium is destroyed by stellar processing (stars fuse D into He), so any observed primordial deuterium must pre-date stars; its survival further demonstrates a primordial (Big Bang) origin for the light elements [1].
Limitation and improvement (2 marks): One limitation is that the helium mass fraction was measured in a single nearby dwarf galaxy; systematic errors such as local stellar enrichment or errors in spectroscopic modelling could bias the result [1]. To address this, the measurement should be repeated in multiple independent metal-poor environments (e.g. extragalactic H II regions of varying metallicities) and extrapolated to zero metallicity to isolate the primordial component, improving statistical robustness [1].
Marking criteria summary (9 marks): 1 = correct interpretation of $z = 6.5$ as lookback time/early universe epoch; 1 = CMB temperature agreement with prediction stated and linked to expansion; 1 = correct assessment of anisotropy implications; 1 = $Y$ compared quantitatively against prediction (within error bars) and assessed as supporting BBN; 1 = error-bar reasoning or significance comment; 1 = D/H as baryon density constraint; 1 = D destruction by stars ⇒ primordial origin; 1 = valid limitation (single site / systematic error); 1 = improvement (multiple sites / metallicity extrapolation).
Q2 — Sample Band 6 response (8 marks), annotated
Scientific meaning of “theory” (1 mark): In science, a theory is not a guess — it is a well-tested, explanatory framework supported by multiple independent lines of evidence that has survived attempts to falsify it. The Big Bang theory is one of the most rigorously tested theories in modern physics, making quantitative predictions that have been confirmed to high precision across several independent observations [1].
Countering the “galaxies through space” claim (2 marks): A conventional explosion drives fragments outward through space, so we would expect nearby galaxies to be moving faster (closest to the centre of explosion) and the distribution of velocities would depend on direction. Instead, Hubble’s law shows that recession velocity is proportional to distance in every direction, with no preferred centre [1]. Furthermore, in a conventional explosion, after enough time has passed, the fragments would slow down (gravity) and distant galaxies would be less redshifted. Cosmological redshift is caused by the expansion of space itself stretching wavelengths as photons travel — a physical mechanism that a conventional Doppler model cannot replicate for very high-$z$ objects [1].
Countering the CMB-from-stars claim (2 marks): First, stellar radiation is not isotropic — it comes from discrete point sources; the CMB is perfectly uniform in all directions to 1 part in 100 000, which no combination of stars could produce [1]. Second, the CMB has a near-perfect black-body (Planck) spectrum at 2.725 K. Stars emit black-body radiation at much higher temperatures (thousands to tens of thousands of kelvin); no combination of stellar spectra sums to a single-temperature black-body at 2.725 K. The CMB can only arise from a hot, dense, thermal-equilibrium state that filled all of space — exactly the early universe described by the Big Bang [1].
Countering the stellar helium claim using deuterium (2 marks): Stellar nucleosynthesis produces helium by fusing hydrogen, but it also destroys deuterium: stars are too hot for deuterium to survive. The observed primordial deuterium abundance ($D/H \approx 2.6 \times 10^{-5}$) cannot have been produced in stars — it is a relic of conditions lasting only minutes in the early universe. Moreover, to produce the observed helium fraction entirely through stars would require burning an enormous amount of hydrogen, which would produce far more heavy elements (carbon, oxygen, iron) than are observed in metal-poor halo stars. The observed H/He/D abundances match BBN predictions without any stellar contribution [2 — award 1 for deuterium argument and 1 for heavy-element overproduction argument].
Convergence of evidence (1 mark): The most powerful aspect of the Big Bang evidence is that three completely independent observations — the expansion of space from galaxy spectra, the CMB from radio telescopes, and light-element abundances from spectroscopy — all converge on the same model with the same parameters (baryon density, age, temperature). The probability that three unrelated phenomena would all coincidentally produce the same cosmological model is negligibly small; their convergence is compelling evidence that the Big Bang model accurately describes reality [1].
Marking criteria summary (8 marks): 1 = correct scientific definition of “theory” vs hypothesis/guess; 1 = Hubble’s law isotropy (no preferred centre); 1 = cosmological redshift as space expansion not particle motion; 1 = CMB isotropy argument against stellar radiation; 1 = CMB black-body argument; 1 = deuterium destroyed by stellar processing / primordial origin; 1 = heavy-element overproduction argument or baryon density argument; 1 = convergence of three independent lines of evidence.