Year 12 PhysicsModule 8⏱ ~20 min5 MC · 2 Short AnswerLesson 2 of 17
Evidence for the Big Bang
You'll be able to calculate redshift from spectra.
In 1992, NASA's COBE satellite mapped the CMB temperature across the full sky for the first time. The satellite found the CMB to be uniform to 1 part in 100,000 at 2.725 ± 0.002 K, with tiny anisotropies of ΔT/T ≈ 10⁻⁵ representing the primordial density fluctuations that seeded galaxy formation. John Mather and George Smoot were awarded the Nobel Prize in Physics in 2006 for this work. COBE's result confirmed that the Big Bang model alone, not any steady-state alternative, correctly predicts the three independent pillars: Hubble expansion, CMB, and primordial nucleosynthesis ratios.
Today's hook: In 1992, NASA's COBE satellite, launched in November 1989, mapped the microwave sky at a resolution of 7° and found the CMB temperature to be 2.725 ± 0.002 K in every direction, with tiny fluctuations of only ΔT/T ≈ 10⁻⁵. George Smoot described it as "like seeing the face of God." What did these one-in-100,000 temperature ripples, the largest structures ever detected, tell cosmologists about the origin of galaxies?
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You’re here
Orient and predict
Bring back what you already know about redshift, the microwave background and the light elements, then commit to a prediction.
Warm up first
Three quick questions from earlier lessons. Pulling old material back to mind before you learn something new makes the new material stick better, so this is not busywork.
Worksheets
Practise this lesson
Four printable worksheets that build from the foundations up to exam-style questions, start at whatever level suits you.
Scientists observe that distant galaxies are redshifted, the CMB has a black-body spectrum at 2.7 K, and the universe is about 75% hydrogen and 25% helium by mass.
Before reading on, answer:
What does redshift of galaxies tell us about the motion of the universe?
Why is the CMB temperature of 2.7 K significant? What would a steady-state universe predict?
Why does the helium abundance matter? Could stars have made all the helium we see?
Warm-up, which of the following is NOT one of the three main lines of evidence for the Big Bang?
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Set your goals and vocabulary
Know what you are aiming for, and get the five terms you need before the evidence arrives.
Learning Intentions
goals
Know, Three Pillars of Evidence
Cosmological redshift / expansion
Cosmic Microwave Background
Primordial nucleosynthesis (H/He ratio)
Understand, Redshift and Expansion
$z = \Delta\lambda/\lambda_{\mathrm{rest}}$
Cosmological vs Doppler redshift
Lookback time vs distance
Can Do, Analyse Observational Data
Calculate redshift from spectra
Estimate distance from recession velocity
Compare model predictions to data
Scan these before reading
vocab
Redshift ($z$)$z = (\lambda_{\mathrm{obs}} - \lambda_{\mathrm{rest}})/\lambda_{\mathrm{rest}}$; a measure of how much a spectral line has been stretched toward longer (redder) wavelengths.
Lookback timeThe time light has been travelling from a distant object to reach us; we see the object as it was in the past.
Cosmic Microwave Background (CMB)Uniform thermal radiation filling all of space, a relic of the hot early universe; temperature 2.725 K.
Primordial nucleosynthesisThe production of H, He and trace Li in the first few minutes after the Big Bang when the universe was hot and dense enough for nuclear fusion.
Hubble constant ($H_0$)The proportionality constant in Hubble's law: $H_0 \approx 70$ km/s/Mpc. Relates recession velocity to distance.
Cross-lesson links: L01 introduced the Big Bang model. L02 evaluates its evidence base, CMB, Hubble expansion, and primordial nucleosynthesis ratios. Scientists accept the Big Bang not from a single experiment but from three independent lines converging on the same model. This multi-evidence approach is the standard for any physical cosmology question.
Core Content
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Evidence 1, redshift and expansion
Define redshift, link it to Hubble's law and read what a stretched spectral line is telling you.
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Pillar 1: Cosmological Redshift and Expansion
+5 XP
The universe is getting bigger
Point a spectrograph at any distant galaxy and you will observe that its hydrogen emission lines arrive at slightly longer wavelengths than the same lines measured in a laboratory on Earth. The further the galaxy, the larger the shift. In the 1920s, Edwin Hubble systematically measured this pattern for dozens of galaxies and found that recession velocity and distance are proportional, Hubble's law: $v = H_0 d$, where $H_0 \approx 70$ km/s/Mpc. Critically, this does not mean galaxies are moving through space away from us, it means space itself is expanding, carrying galaxies with it.
For small $z$ (nearby galaxies), $v \approx cz$. For large $z$ (distant galaxies), the relationship is more complex because the expansion rate has changed over time. The most distant galaxies observed have $z > 10$.
Figure 1, Spectral lines from a distant galaxy are redshifted compared to laboratory measurements; the shift is proportional to the galaxy's distanceText description
Two spectra on the same wavelength axis, each with the same three absorption lines.
Laboratory source: the lines at their rest wavelengths, λrest.
Distant galaxy: every line is shifted to a longer wavelength, λobs = (1 + z)λrest, a redward shift with z > 0 (drawn for z = 0.1). The shift grows with the galaxy’s distance.
Stop & Check
A galaxy has spectral lines shifted from 500 nm (rest) to 550 nm (observed). Calculate its redshift $z$. Using Hubble's law with $H_0 = 70$ km/s/Mpc, estimate its distance. (Assume $v = cz$ for this approximation.)
Cosmological redshift ($z = (\lambda_{\mathrm{obs}}-\lambda_{\mathrm{rest}})/\lambda_{\mathrm{rest}}$) shows that more distant galaxies recede faster, giving Hubble's law $v = H_0 d$ ($H_0 \approx 70$ km/s/Mpc). This means space itself is expanding; distance follows from $d = cz/H_0$ for $z \ll 1$.
Pause, copy the highlighted definition and formula into your book before moving on.
A spectral line with rest wavelength 500 nm is observed at 525 nm from a distant galaxy. What is the redshift $z$?
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Evidence 2, the cosmic microwave background
Trace the CMB back to recombination and test what a steady-state universe would have to predict.
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Pillar 2: The Cosmic Microwave Background
+5 XP
The fossil radiation from the early universe
We just saw that cosmological redshift and Hubble's law give us the first pillar of Big Bang evidence, the universe is expanding. That raises a question: is there direct observational evidence of the hot early state itself, not just its expansion? This card answers it → yes, the CMB is the thermal afterglow of that hot early universe, detected as uniform microwave radiation at 2.725 K.
Discovered accidentally by Penzias and Wilson in 1965, the CMB is uniform black-body radiation coming from all directions. Its perfect thermal spectrum at 2.725 K is exactly what the Big Bang model predicts for cooled relic radiation released at recombination when the universe cooled enough (~380,000 years after the Big Bang) for protons to capture electrons and form neutral hydrogen, allowing photons to travel freely for the first time.
Key features of the CMB:
Black-body spectrum: The CMB peaks at ~160 GHz (~1.9 mm wavelength), corresponding to $T = 2.725$ K. This is precisely what the Big Bang model predicts for cooled relic radiation.
Isotropy: The temperature is the same in all directions to about 1 part in 100,000. This uniformity is consistent with a hot, dense early state.
Anisotropies: The tiny temperature fluctuations ($\Delta T/T \sim 10^{-5}$) are the density perturbations that seeded the formation of galaxies and clusters.
Satellites COBE (1992), WMAP (2003) and Planck (2013) have mapped the CMB with extraordinary precision, and every measurement confirms Big Bang predictions. The steady-state model has no mechanism to produce a uniform thermal background at a specific temperature, the CMB is fatal for steady-state cosmology.
Stop & Check
Explain why the discovery of the CMB in 1965 was fatal for the steady-state theory of the universe. Your answer should refer to what the steady-state model would predict.
The CMB is relic black-body thermal radiation (2.725 K) released around recombination and photon decoupling ~380,000 years after the Big Bang, isotropic to about 1 part in 100,000. Its spectrum and uniformity are strong evidence for a hot, dense early universe and are incompatible with the classic steady-state model's predictions; tiny anisotropies ($\Delta T/T \sim 10^{-5}$) seeded later structure.
Add the highlighted principle to your notes before the check below.
The CMB has a perfect black-body spectrum at approximately 2.725 K, which is consistent with cooled relic radiation from the hot early universe.
The steady-state model of the universe predicts a uniform thermal background radiation at a specific temperature because matter is continuously created throughout space.
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Evidence 3, primordial abundances
Compare the observed hydrogen to helium ratio with what Big Bang nucleosynthesis predicts, and see why stars cannot stand in for it.
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Pillar 3: Primordial Nucleosynthesis
+5 XP
The abundances of light elements
We just saw that the CMB is the second independent pillar of Big Bang evidence, direct thermal radiation from the early universe. That raises a question: is there a third, completely independent line of evidence that doesn't rely on radiation at all? This card answers it → yes, the observed hydrogen-to-helium abundance ratio (~75%:25%) precisely matches Big Bang nucleosynthesis predictions, which no steady-state model can explain.
In the first few minutes after the Big Bang, the universe was hot and dense enough for nuclear fusion. Protons and neutrons combined to form light nuclei. The Big Bang model predicts the resulting abundances based on the density of baryonic matter and the expansion rate. The observed abundances match the predictions remarkably well.
Predicted and observed light-element abundances:
Hydrogen-1 (protium): ~75% by mass, the dominant product
Helium-4: ~25% by mass, formed from nearly all available neutrons
Trace deuterium, helium-3 and lithium-7: ~0.01% combined
The match works only for a specific baryon density, which is independently confirmed by CMB anisotropy measurements. This cross-check between two independent observations is one of the most powerful confirmations of the Big Bang model.
Why stars cannot account for the helium: Stars also produce helium through fusion, but stellar nucleosynthesis would overproduce heavier elements (particularly carbon and oxygen) and leave a different deuterium abundance. The primordial helium abundance (~25%) is too high to have been produced by stars, and the deuterium abundance is too delicate, stars destroy deuterium rather than producing it.
Figure 2, Timeline of primordial nucleosynthesis: within the first ~20 minutes the universe produced essentially all the hydrogen and helium it would ever haveText description
Time after the Big Bang: 0.01 s, protons and neutrons are free. 1 s, neutrinos decouple. About 3 minutes, helium-4 and deuterium form. About 20 minutes, nucleosynthesis ends.
Result: about 75% hydrogen, about 25% helium-4, and traces of deuterium, helium-3 and lithium-7.
This was predicted by the Big Bang model and is confirmed by observations of old, unprocessed gas clouds.
Stop & Check
The observed helium mass fraction in old, unprocessed gas clouds is ~24%. Big Bang nucleosynthesis predicts ~25% for the observed baryon density. Why does this agreement support the Big Bang, and why can't stars alone explain it?
Primordial nucleosynthesis in the first ~20 minutes produced ~75% H and ~25% He-4 by mass (plus trace D, He-3, Li-7); these abundances match Big Bang predictions precisely. Stars cannot account for the helium because stellar fusion overproduces carbon and oxygen and destroys deuterium rather than preserving it.
Pause, write the highlighted key facts into your book before the check below.
The observed abundance of light elements (mainly H and He) supports the Big Bang because:
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Apply and evaluate the evidence
Work the redshift calculations, weigh each pillar against the steady-state model, then pull all three lines together.
HSC Tip: The Three Pillars
In exam questions about Big Bang evidence, always mention all three pillars: (1) expansion/redshift, (2) CMB, and (3) primordial nucleosynthesis. Each provides independent confirmation, together they form a robust case.
A common trap: confusing lookback time with the age of the universe. A galaxy at distance $d$ has lookback time $t \approx d/c$, but the light was emitted when the universe was younger than its current age. For $z > 1$, the relationship between distance, redshift and lookback time becomes non-linear.
Activity 1, Redshift Calculations
ApplyBand 4
Use $z = \Delta\lambda/\lambda_{\mathrm{rest}}$ and Hubble's law to find distances
A galaxy's H-alpha line (rest wavelength 656.3 nm) is observed at 679.3 nm. Calculate $z$ and estimate the recession velocity. Is the low-$z$ approximation $v \approx cz$ valid here?
Using $H_0 = 70$ km/s/Mpc and your recession velocity from (1), estimate the galaxy's distance in Mpc and in light-years (1 Mpc $\approx 3.26 \times 10^6$ ly).
A quasar has $z = 3.0$. Discuss whether the formula $v = cz$ can be used to find its recession velocity. What does $z = 3.0$ imply about when this object's light was emitted?
Activity 2, Evaluating the Evidence
AnalyseBand 5
Assess the strength of each Big Bang pillar
For each of the three pillars of Big Bang evidence, complete the table by answering: (a) What is observed? (b) What does the Big Bang model predict? (c) What does the steady-state model predict (or fail to predict)?
Cosmological redshift: state what is observed, what the Big Bang predicts, and whether a steady-state model can explain it.
CMB: state the key observational features, what the hot Big Bang model predicts, and why the evidence strongly contradicts classic steady-state cosmology.
Primordial nucleosynthesis: state the observed H/He ratio, what the Big Bang predicts, and why stellar nucleosynthesis alone cannot account for it.
Synthesis, connect the ideas
In this lesson, three independent lines of evidence converge:
Redshift of galaxies: space is expanding, trace back and the universe was once a single hot, dense point.
CMB: relic thermal radiation at 2.725 K is the "afterglow" of that hot early state, invisible to any model that doesn't start with a Bang.
Primordial nucleosynthesis: the H/He ratio is a "fingerprint" of conditions in the first minutes, independently confirmed by CMB baryon density measurements.
No cosmological model other than the Big Bang explains all three simultaneously.
Assess7 marks
Assess the extent to which the three main lines of evidence for the Big Bang model together provide stronger support than any one of them alone. (7 marks)
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Set the criterion you will judge against
An assess answer needs a stated standard. Without one you can only list, and a list cannot answer "to what extent".
Evidence is stronger in combination when each line is independent of the others and when a rival model would have to explain all of them at once.
The criterion is doing the work: independence plus joint constraint. Name it first so every paragraph after this has something to be measured against.
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Take each line and say what it establishes on its own
Deal with all three, briefly. The point of this step is what each one does NOT settle by itself.
Cosmological redshift shows the Universe is expanding, so it was denser in the past, but expansion alone does not require a hot beginning. The cosmic microwave background is a near-uniform blackbody spectrum, which shows the early Universe was hot and in thermal equilibrium. The abundance of light elements, about 25 per cent helium by mass, shows conditions once suited nuclear fusion throughout space.
Three lines, three distinct conclusions: that it expanded, that it was hot, and that it was dense enough to fuse. Keeping them separate is what makes the next step possible.
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Show the lines are independent
Independence is the first half of your criterion, so it needs its own step.
These rest on unrelated measurements, made with different instruments: galaxy spectra, microwave radiometry and stellar and interstellar composition. An error in one would not propagate into the others.
This is the step most answers miss. Three agreeing measurements of the same quantity are weaker than three independent measurements of different quantities that a single model must reconcile.
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Apply the joint constraint to a rival
The clearest way to show combination matters is to make a rival model try to pass all three tests.
A steady-state model can accommodate expansion by continuous creation of matter, so the first line alone does not decide between the models. But it has no source for a near-uniform blackbody background filling all space, and no epoch in which the light element abundances could be set. Expansion is consistent with both models; all three together are consistent with only one.
This is the assessment. A rival that survives one test and fails the other two demonstrates the combination is stronger, rather than merely asserting it.
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Qualify the judgement honestly
An assess answer that finds no limitation has usually not looked. State what the evidence does not establish.
The support is strong but not unlimited: these three lines constrain the hot, dense, expanding early state, and do not provide a tested account of the initial instant itself.
Precision about the scope of a claim is a band-6 habit, and this lesson makes the same point. Claiming the evidence proves more than it does costs marks.
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The full-mark answer
Criterion, then each line, then independence, then a rival tested against all three, then the limit.
Evidence is stronger in combination when each line is independent and when a rival model must explain all of them at once. Cosmological redshift shows the Universe is expanding and so was denser in the past, but does not by itself require a hot beginning. The cosmic microwave background is a near-uniform blackbody spectrum, showing the early Universe was hot and in thermal equilibrium. The light-element abundances, about 25 per cent helium by mass, show conditions throughout space once suited nuclear fusion. These rest on unrelated measurements made with different instruments, so an error in one would not propagate into the others. A steady-state model can accommodate expansion through continuous creation, so the first line alone does not decide between the models, but it has no source for a uniform blackbody background filling all space and no epoch in which the light-element abundances could be set. Expansion is consistent with both models; all three together are consistent with only one, which is the sense in which the combination is decisive. The support is nonetheless bounded: it constrains the hot, dense, expanding early state rather than providing a tested account of the initial instant.
Seven marks. The judgement is earned by putting a named rival through all three tests, and it is bounded at the end rather than overstated.
Analyse6 marks
Analyse how the observed abundance of helium in the Universe provides evidence for primordial nucleosynthesis rather than for production in stars alone. (6 marks)
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State the observation as a number and a pattern
The evidence here is quantitative and, just as importantly, uniform. Both features matter.
Helium makes up about 25 per cent of the ordinary matter in the Universe by mass, and this proportion is close to the same everywhere we measure it.
Two properties, not one. The amount is the first constraint and the uniformity is the second, and the argument needs both.
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Test the rival explanation against the amount
Stars do make helium, so the stellar explanation has to be defeated on evidence rather than dismissed.
Stars do fuse hydrogen into helium, but summing the output of all the stars that have existed over the age of the Universe falls far short of 25 per cent.
The quantitative shortfall is the load-bearing point. "Stars also make helium" without the amount concedes the question.
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Test the rival against the uniformity
The second property attacks the same explanation from a different direction, which is what makes the analysis strong.
Stellar production would also leave a signature of where the stars were: old, metal-poor regions that have formed few stars should be helium-poor. They are not, showing a floor of helium that predates star formation.
Naming the prediction that fails is the analytical step. An explanation is tested by what it implies, not only by its total.
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Give the mechanism the evidence points to
Having ruled out the alternative, supply the positive account.
A hot, dense early Universe provides one: for a few minutes the whole of space was hot and dense enough for fusion, so protons and neutrons combined into helium everywhere at once before expansion cooled it below the threshold and the reactions stopped.
"Everywhere at once" explains the uniformity and "for a few minutes" explains why the process stopped rather than consuming all the hydrogen.
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Draw the implication precisely
Finish on what the evidence establishes, in the terms the question set.
The abundance therefore records conditions before any star existed, and stellar fusion adds to a primordial floor rather than accounting for it.
The conclusion distinguishes "stars contribute" from "stars are sufficient", which is exactly the distinction the question asks for.
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The full-mark answer
Observation, rival tested on amount, rival tested on distribution, mechanism, implication.
Helium makes up about 25 per cent of the ordinary matter in the Universe by mass, and this proportion is close to the same everywhere we measure it. Stars do fuse hydrogen into helium, but the summed output of all stars over the age of the Universe falls far short of 25 per cent. Stellar production would also predict a signature of where the stars were, so old, metal-poor regions that have formed few stars should be helium-poor; they are not, indicating a floor of helium that predates star formation. A hot, dense early Universe supplies both features: for a few minutes the whole of space was hot and dense enough for fusion, so protons and neutrons combined into helium everywhere at once, until expansion cooled it below the threshold and the reactions stopped. The observed abundance therefore records conditions before any star existed, and stellar fusion adds to a primordial floor rather than accounting for it.
The analysis works by making the rival explanation produce two predictions and showing both fail, then supplying a mechanism that produces both observations.
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Independent practice
Show what you can do without prompts
Work a shuffled question-bank set, then write the two HSC-style evidence responses.
Quick recall, evidence for the Big Bang
+5 XP
A fresh five-question set drawn from this lesson's bank, feedback shown immediately. +5 XP per correct · +25 XP all correct
Pick your answer, then rate your confidence, that tells the system what to drill next.
Short Answer
+5 XP
ApplyBand 5(5 marks) 1. (a) Outline the three main lines of evidence supporting the Big Bang theory. (b) A galaxy shows a spectral line at 660 nm that has rest wavelength 600 nm. Calculate the redshift and, using Hubble's law ($H_0 = 70$ km/s/Mpc), estimate its distance. (c) Explain why the CMB is described as a black-body spectrum and why this is significant evidence. (d) Why can't stars alone account for the observed helium abundance in the universe?
1 mark each: (a) three pillars named, (b) correct z and d, (c) black-body significance, (d) stellar limitation
AnalyseBand 6(4 marks) 2. (a) Describe what is meant by the "steady-state" model of the universe. (b) For each of the three pieces of Big Bang evidence (redshift, CMB, nucleosynthesis), explain whether the steady-state model can account for the observation, and why or why not. (c) Based on your analysis, evaluate whether the steady-state model is a viable scientific theory.
1 mark: steady-state definition · 1 mark per piece of evidence evaluated (up to 3) · synthesis/evaluation in (c)
Show all answers
Multiple choice
MC answers and full explanations are shown inline as you complete each question. Use the retry button to attempt a fresh set drawn from the lesson bank.
Short Answer, Model Answers
Q1 (5 marks): (a) Three pillars: (1) cosmological redshift, distant galaxies are receding and the recession velocity is proportional to distance; (2) the CMB, a uniform thermal background at 2.725 K consistent with cooled relic radiation; (3) primordial nucleosynthesis, the observed ~75% H / ~25% He ratio matches Big Bang predictions (1 mark). (b) $z = (660 - 600)/600 = 0.10$; $v = cz = 3.0\times10^5 \times 0.10 = 3.0\times10^4$ km/s; $d = v/H_0 = 3.0\times10^4/70 \approx 429$ Mpc (1 mark). (c) The CMB has a perfect black-body spectrum, the intensity-versus-frequency curve follows Planck's radiation law for a body at 2.725 K. This is significant because only a hot, dense early universe followed by billions of years of expansion would produce such a spectrum; no other cosmological model predicts it (1 mark). (d) Stars cannot account for all the helium because stellar fusion also produces carbon and oxygen; if all helium were made by stars, much more carbon would be observed than is measured. Additionally, stars destroy deuterium rather than producing it, but primordial deuterium is observed in old, unprocessed gas clouds (1 mark).
Q2 (4 marks): (a) The steady-state model proposes that the universe has no beginning or end; as galaxies move apart, new matter is continuously created to maintain a constant average density, so the universe appears the same at all times and in all places (1 mark). (b) Redshift: the steady-state model can explain recession, but it requires the universe to always have been expanding at the same rate, it cannot explain why the expansion rate was different in the early universe without invoking a Big Bang. CMB: the steady-state model has no mechanism to produce a uniform thermal background at a specific temperature, this observation alone is fatal for steady-state cosmology (1 mark). Nucleosynthesis: the steady-state model has no early hot dense phase, so it cannot predict the observed H/He ratio; stars alone overproduce heavier elements and destroy deuterium (1 mark). (c) The steady-state model is not viable because it fails to account for all three independent observations. A scientific theory must explain all available evidence; steady-state fails on two independent counts (CMB and nucleosynthesis) while the Big Bang model explains all three. The steady-state model was formally abandoned after the discovery of the CMB in 1965 (1 mark).
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Final step
Retrieve, reflect and finish
Check what actually stuck, revisit your opening predictions and record what you now believe.
Check what actually stuck
How did your thinking change?
At the start you were asked about the COBE satellite's 1992 discovery of CMB anisotropies at ΔT/T ≈ 10⁻⁵, the temperature ripples that John Mather and George Smoot identified as the seeds of large-scale structure. Review your predictions:
Did you predict that the COBE temperature fluctuations of 1 part in 100,000 represent the primordial density variations that eventually grew into galaxies and galaxy clusters? Correct, denser regions in the early universe gravitationally attracted more matter, growing over 13.8 billion years into the structures we observe today.
Did you predict that the CMB temperature of 2.725 K is significant because it matches the cooled relic radiation from the Big Bang? Correct, a steady-state universe would not produce a uniform thermal background at a specific temperature.
Did you predict that stars cannot account for all helium because they would overproduce heavier elements? Correct, the primordial helium abundance (~25%) is too high and deuterium too fragile to be explained by stellar fusion alone.