Evidence for the Big Bang
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.
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?
Know — Three Pillars of Evidence
- Cosmological redshift / expansion
- Cosmic Microwave Background
- Primordial nucleosynthesis (H/He ratio)
Understand — Redshift and Expansion
- $z = \Delta\lambda/\lambda_{rest}$
- 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
Core Content
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.
The redshift $z$ is defined as:
$z = \dfrac{\lambda_{obs} - \lambda_{rest}}{\lambda_{rest}} = \dfrac{\lambda_{obs}}{\lambda_{rest}} - 1$
$v = H_0 d$ ($H_0 \approx 70$ km/s/Mpc)
$v \approx cz$ (for $z \ll 1$, i.e. nearby galaxies)
$t_{lookback} \approx d/c$ (approximate lookback time)
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 distance
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 ($z = (\lambda_{obs}-\lambda_{rest})/\lambda_{rest}$) 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 $z$?
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.
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 at recombination ~380,000 years after the Big Bang, isotropic to 1 part in 100,000. The steady-state model predicts no such background, so the CMB's existence definitively disproves it; tiny anisotropies ($\Delta T/T \sim 10^{-5}$) are the seeds of today's galaxies.
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.
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 have
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:
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.
Use $z = \Delta\lambda/\lambda_{rest}$ 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?
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 Big Bang predicts, and why this disproves 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.
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.
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.
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)
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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).
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.