Physics • Year 12 • Module 8 • Lesson 1
The Big Bang Theory
Build HSC Band 5–6 extended-response technique on evaluating cosmological evidence, applying the redshift formula, and designing an investigation into the CMB.
1. Data + scenario: COBE satellite CMB observations (Band 5–6)
8 marks Band 5–6
Scenario. In 1989, NASA launched the Cosmic Background Explorer (COBE) satellite, which was designed to measure the spectrum and spatial distribution of the CMB across the whole sky. COBE produced two landmark results:
- The CMB spectrum matched a perfect black-body curve at T = 2.725 K with no measurable deviation — the most perfect black-body spectrum ever observed.
- The CMB was extraordinarily uniform across the sky, with tiny temperature fluctuations of only ±0.00003 K (30 μK) on top of the 2.725 K average — an anisotropy of roughly 1 part in 100,000.
Before COBE, one prominent alternative to the Big Bang was the Steady State theory, which proposed that the universe has no beginning or end and that new matter is continuously created as space expands, maintaining a constant average density. The Steady State theory predicts no CMB (since there was no hot, dense early phase) and no large-scale structure arising from primordial density fluctuations.
The table below summarises simplified COBE data.
| Measurement | COBE observation | Big Bang prediction | Steady State prediction |
|---|---|---|---|
| CMB spectrum type | Perfect black body at 2.725 K | Black body (relic thermal radiation) | No CMB expected |
| Temperature uniformity | Uniform to 1 in 100,000 (±30 μK) | Near-uniform (slight anisotropies predicted) | No prediction |
| Temperature anisotropies | ±30 μK fluctuations detected | Tiny fluctuations = seeds of structure | Not predicted |
| Spectrum peak wavelength | ~1.9 mm (microwave) | Microwave (redshifted visible/IR from 3000 K) | Not applicable |
Data based on: COBE Science Team (1992). Mather et al., ApJ; Smoot et al., ApJ.
Q1. Analyse and evaluate the COBE data to assess the extent to which the observations support the Big Bang theory and challenge the Steady State theory. In your response you must:
- Explain how the black-body spectrum of the CMB supports the Big Bang model, with reference to the physical origin of the CMB at recombination.
- Explain the significance of the tiny temperature anisotropies in the CMB for our understanding of large-scale cosmic structure.
- Use at least two specific pieces of data from the table to evaluate whether the Steady State theory is consistent with the observations.
- Assess one limitation of using the CMB alone as evidence for the Big Bang and suggest one additional line of evidence that strengthens the model.
- Calculate the redshift z of the CMB photons, given they were emitted at Temit = 3000 K and observed at Tobs = 2.725 K. Show your working.
2. Experimental design — investigating whether the CMB is truly uniform (Band 5–6)
7 marks Band 5–6
Research question. A physics student claims that the Cosmic Microwave Background is not perfectly uniform and that its tiny temperature variations prove the universe was structured from the very beginning. Design a scientific investigation to test whether the CMB temperature varies measurably across different regions of the sky, and explain how the results would be used to evaluate this claim.
Context: You have access to a ground-based microwave antenna/receiver capable of detecting intensity variations in the microwave frequency range (~160 GHz), a steerable telescope mount, a sensitive bolometer detector, and data-analysis software. Atmospheric interference can be reduced by observing during local winter at a high-altitude, dry site (e.g. Atacama Desert, Chile).
Q2. Design the investigation and present it in the format below.
- State a testable hypothesis, including the independent and dependent variables.
- Identify the independent variable, dependent variable, and at least two controlled variables.
- Describe the procedure in at least four numbered steps, including how you would account for sources of error (atmospheric emission, instrumental noise).
- Explain what result would support the student’s claim and what result would falsify it.
- State two limitations of the ground-based design and explain why space-based observation (as used by COBE/WMAP/Planck) is superior.
Q1 — Sample Band 6 response (8 marks), annotated
CMB black-body spectrum and Big Bang support: The COBE observation of a perfect black-body spectrum at 2.725 K strongly supports the Big Bang model [1 — links observation to model]. During the Big Bang, the universe was an extremely hot, dense plasma in which photons and matter were in thermal equilibrium. At recombination (~380,000 years after the Big Bang, T ≈ 3000 K), electrons combined with nuclei to form neutral hydrogen; the universe became transparent and photons decoupled, streaming freely as thermal radiation. As the universe expanded, these photons were cosmologically redshifted: using λobs = λemit(1 + z) and z ≈ 1099, the visible/IR radiation has been stretched to microwave wavelengths, consistent with the observed 2.725 K temperature. The perfect black-body shape arises because the photons were in complete thermal equilibrium with matter before decoupling — a condition that only the Big Bang model predicts [1 — physical origin explained].
Significance of temperature anisotropies: The tiny ±30 μK fluctuations in the CMB are the imprint of quantum density fluctuations in the early universe, amplified by inflation and gravity. Regions slightly denser than average would later gravitationally attract more matter, forming the seeds of galaxies, galaxy clusters, and the large-scale cosmic web observed today. Without these anisotropies, the universe would be perfectly uniform and no large-scale structure could have formed [1].
Evaluation of Steady State theory: The Steady State theory predicts no CMB because it posits no hot, dense early phase; instead, new matter is continuously created. The COBE data directly contradict this: a perfect black-body CMB at 2.725 K is observed, which requires a thermal equilibrium phase — consistent only with a hot, dense early universe [1]. Furthermore, the Steady State theory makes no prediction about temperature anisotropies or microwave radiation from space, so the detection of structured ±30 μK fluctuations across the sky — consistent with Big Bang structure-formation models — provides a second piece of evidence inconsistent with the Steady State theory [1]. The observations therefore strongly challenge the Steady State model.
Limitation and additional evidence: A limitation of using the CMB alone is that the black-body spectrum could, in principle, be produced by some other thermal source not predicted by the Big Bang; the CMB is correlational evidence rather than direct observation of the early universe. An additional line of evidence is the observed abundances of light elements (hydrogen ~75%, helium ~25%, trace lithium), which match the predictions of Big Bang nucleosynthesis to within observational uncertainty — an independent quantitative confirmation of the Big Bang model that does not rely on the CMB [1].
Redshift calculation: T ∝ 1/a and λ ∝ a, so λobs/λemit = Temit/Tobs = 3000 / 2.725 ≈ 1100. Since 1 + z = λobs/λemit = 1100, z ≈ 1099 [1 — method and answer].
Marking criteria summary (8 marks): 1 = black-body spectrum linked to Big Bang (thermal equilibrium at recombination); 1 = physical origin of CMB explained (recombination, neutral H, photon decoupling, redshift to microwaves); 1 = significance of anisotropies for large-scale structure formation; 1 = evaluates Steady State against first COBE data point (no CMB expected); 1 = uses second data point to further challenge Steady State; 1 = identifies one valid limitation of CMB-only evidence; 1 = names one valid additional line of evidence (nucleosynthesis abundances, Hubble expansion, large-scale structure); 1 = correct redshift calculation z ≈ 1099 with working.
Q2 — Sample Band 6 response (7 marks), annotated
Hypothesis: If the CMB has measurable temperature anisotropies, then the microwave intensity detected by a steerable antenna will vary by approximately 30 μK between different sky directions after correcting for systematic errors. Independent variable: direction of the antenna on the sky (right ascension and declination). Dependent variable: microwave intensity/temperature measured at 160 GHz. Controlled variables: observing frequency (160 GHz); integration time per sky position (equal for each position); atmospheric conditions (observe only on dry, stable nights); electronic gain of the receiver (calibrated against a blackbody reference load before and after each observation). [1 — hypothesis with IV and DV; 1 — controlled variables]
Procedure: (1) Calibrate the microwave receiver against a blackbody reference load at known temperature to determine the system noise temperature and gain. (2) Divide the sky into a grid of pointing positions separated by 1°. For each position, integrate the received signal for 60 seconds, recording the output voltage proportional to microwave intensity. (3) Correct raw data for atmospheric emission by performing a sky-dip measurement (tilting the antenna from zenith to low elevation to characterise atmospheric contribution) and subtracting it from each data point. (4) Convert corrected intensities to antenna temperatures and compare across all sky positions to map any spatial variation. Repeat each sky position three times on different nights to test repeatability and reduce random noise. [1 — four clear steps; 1 — error correction method included]
Interpretation: Result supporting the claim: detected temperature variations of ~30 μK above the noise floor, with spatial patterns inconsistent with instrumental or atmospheric noise, would support the existence of genuine CMB anisotropies. Result falsifying the claim: if sky temperatures are uniform to within measurement uncertainty, this would not support the claim of primordial structure. [1]
Limitations and space-based superiority: Limitation 1: Ground-based microwave observation is contaminated by atmospheric water vapour, which emits and absorbs at microwave frequencies, masking small signals. The ~30 μK anisotropies are smaller than typical atmospheric fluctuations. Limitation 2: A ground-based telescope has a limited field of view; it cannot observe the full sky in a single session, and the Milky Way foreground limits observations near the Galactic plane. [1 — two valid limitations] Space-based observatories such as COBE, WMAP, and Planck operate above the atmosphere, eliminating atmospheric noise; they can observe the full sky continuously; they achieve millikelvin sensitivity unattainable from the ground. [1 — space-based superiority with physical explanation]
Marking criteria summary (7 marks): 1 = testable hypothesis naming IV and DV; 1 = two or more controlled variables (frequency, integration time, atmosphere, gain); 1 = four clear procedural steps; 1 = method to correct for atmospheric or instrumental error; 1 = correct statement of what result would support and what would falsify; 1 = two valid limitations of ground-based design; 1 = explains why space-based observation is superior with specific physical reasoning.