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In 1929 Edwin Hubble, working with the 100-inch Hooker telescope at Mount Wilson, plotted the recession velocities of two dozen galaxies (measured by Vesto Slipher's spectroscopic redshifts) against their distances (measured via Cepheid variables). The points scattered along a straight line: the further a galaxy lay, the faster it was receding. That graph — Hubble's law — was the first observational evidence that the universe is expanding, and it forced an extraordinary inference: extrapolated backward, all galaxies must once have been together, in a state of extreme density and temperature. The resulting Big Bang picture is now the cornerstone of modern cosmology, supported by three independent lines of evidence: the Hubble expansion itself, the cosmic microwave background (CMB), and the primordial nucleosynthesis of light elements. This lesson develops each pillar in turn, derives the age of the universe from H₀, and notes the remaining open questions.
Spec mapping. This lesson covers AQA 7408 section 3.9.3 on Hubble's law and the Big Bang: v = H₀d as the relation between recession velocity and distance; current values of H₀; the resulting estimate of the age of the universe; the cosmic microwave background as evidence of an early hot dense phase; the abundances of light elements; the qualitative narrative of cosmic evolution from the first second through to galaxy formation. (Refer to the official AQA specification document for exact wording.)
Synoptic links. Hubble's law builds directly on the redshift treatment of the previous lesson. The CMB is a black-body spectrum at T ≈ 2.7 K, applying Wien's law and the Stefan-Boltzmann law of Lesson 3. Primordial nucleosynthesis links to the nuclear physics unit (AQA 3.8) — fusion, binding-energy curves, and neutron-proton interconversion. The 1998 discovery of cosmic acceleration through Type Ia supernovae links to the final lesson on standard candles.
Hubble's law states that the recession velocity v of a galaxy is proportional to its distance d:
v = H₀ d
where H₀ is the Hubble constant — the present-day value of the Hubble parameter, with conventional units of km s⁻¹ Mpc⁻¹. Modern measurements give
H₀ ≈ 67 – 73 km s⁻¹ Mpc⁻¹
with a current best-estimate range. Two principal methods give slightly different values:
The disagreement — known as the Hubble tension — is currently one of the most prominent unsolved problems in cosmology. AQA candidates should quote H₀ as a range (67–73 km s⁻¹ Mpc⁻¹) and may use a round figure of 70 km s⁻¹ Mpc⁻¹ for calculations. Quoting unfeasibly precise values without acknowledging the range is a citation-integrity concern.
The Virgo cluster lies at a distance of about 16.5 Mpc. Estimate its recession velocity using H₀ = 70 km s⁻¹ Mpc⁻¹.
Solution. v = H₀ d = 70 × 16.5 = 1155 km s⁻¹. Observations confirm a mean recession velocity of about 1100 km s⁻¹, in excellent agreement.
A galaxy has a measured redshift z = 0.02. Estimate its distance.
Solution. v ≈ cz = 3.00 × 10⁵ × 0.02 = 6000 km s⁻¹. d = v / H₀ = 6000 / 70 = 86 Mpc (with H₀ = 70 km s⁻¹ Mpc⁻¹).
If the expansion has been at a constant rate (an approximation that ignores both gravitational deceleration in the early universe and dark-energy acceleration today), every galaxy has been moving away at speed v for time
t = d / v = 1 / H₀
This is called the Hubble time. Converting H₀ to SI units (per second):
H₀ ≈ 70 km s⁻¹ Mpc⁻¹ = 70 × 10³ m s⁻¹ / 3.086 × 10²² m = 2.27 × 10⁻¹⁸ s⁻¹
Hubble time t_H = 1 / H₀ ≈ 4.41 × 10¹⁷ s ≈ 14.0 × 10⁹ years
A more rigorous calculation including the universe's deceleration and recent acceleration gives an age of 13.8 billion years. The two agree to within 5% — remarkable, given the approximations.
Repeat the calculation with H₀ = 73 km s⁻¹ Mpc⁻¹.
Solution. H₀ = 73 × 10³ / 3.086 × 10²² = 2.37 × 10⁻¹⁸ s⁻¹. t_H = 1 / H₀ = 4.23 × 10¹⁷ s ≈ 13.4 × 10⁹ years.
This is the Hubble tension in a nutshell: a difference of 6 km s⁻¹ Mpc⁻¹ in H₀ shifts the age estimate by about 0.6 Gyr. With age-dating of the oldest globular clusters now reaching ~13.0 Gyr precision, the gap between the two H₀ measurements has real cosmological consequences.
graph LR
A["Galaxy A<br/>(here, now)"] -->|d_1, v_1| B["Galaxy B<br/>20 Mpc"]
A -->|d_2 = 2d_1, v_2 = 2v_1| C["Galaxy C<br/>40 Mpc"]
A -->|d_3 = 4d_1, v_3 = 4v_1| D["Galaxy D<br/>80 Mpc"]
Every galaxy sees every other galaxy receding, with velocity proportional to distance. This is not because we are at the centre of the universe — by translational symmetry of the Hubble flow, every observer in every galaxy sees the same picture. The classic balloon analogy makes this concrete: paint dots on a balloon and inflate it; from any dot's perspective, all other dots recede, and the further ones recede faster. The dots themselves do not move on the balloon's surface — the surface itself is expanding.
The "no centre" point is essential. The Big Bang did not happen at a particular place in space; it happened everywhere, including the location now occupied by every galaxy. There is no "edge of the universe" beyond which space stops.
If galaxies are receding now, they were closer together in the past — and at some early time the entire observable universe must have been compressed into a region of arbitrarily small size, arbitrarily high density, and arbitrarily high temperature. The standard Big Bang picture traces cosmic history from the earliest moment we can describe with confidence (the end of the Planck era, ~10⁻⁴³ s after the singularity) through to galaxy formation and the present.
| Cosmic age | Temperature | What happened |
|---|---|---|
| 0 | ∞ | Singularity (extrapolation, not observation) |
| 10⁻³⁵ – 10⁻³² s | ~10²⁷ K | Inflation — exponential expansion by factor ≳ 10²⁶ |
| 10⁻⁶ s | 10¹³ K | Quarks confine into protons and neutrons |
| 1 s | 10¹⁰ K | Neutrinos decouple |
| 3 – 20 min | 10⁹ K | Big Bang nucleosynthesis — H and He form |
| 380 000 yr | 3 000 K | Recombination — atoms form, photons decouple, CMB released |
| ~200 Myr | ~30 K | First stars (Population III) — reionisation begins |
| ~1 Gyr | ~15 K | First galaxies form |
| ~13.8 Gyr (now) | 2.725 K | Present day |
Inflation is required to explain the flatness and horizon problems — the observation that the universe is geometrically flat to high precision and that regions of the CMB that were causally disconnected at the time the radiation was emitted are nonetheless at the same temperature. AQA does not require detail on inflation; the key examined milestones are nucleosynthesis, recombination, and the present.
The first piece of evidence is the observation of Hubble's law itself: distant galaxies recede with velocity proportional to distance. Run the expansion backwards, and the universe was once arbitrarily small, dense and hot. This is what the universe is doing now.
In 1965, Arno Penzias and Robert Wilson, working with a Bell Labs horn antenna, found an unexpected microwave signal coming from every direction in the sky at the same temperature. The signal had no preferred direction (it was isotropic), no preferred time of day (it was constant), and had a thermal spectrum corresponding to a temperature of about 3 K. They had inadvertently detected the cosmic microwave background — the relic radiation predicted by Dicke, Peebles, Alpher and Herman.
In the early universe, matter and radiation were in thermal equilibrium. Photons were unable to travel freely because they were scattered repeatedly by the dense plasma of free electrons. As the universe expanded and cooled, at age ~380 000 years (T ~ 3000 K) electrons combined with protons to form neutral hydrogen — the recombination epoch. At that moment the universe became transparent and photons could travel unimpeded. We see those photons today, redshifted by a factor 1 + z ≈ 1100 from their original ~3000 K (peak in the visible) down to ~2.7 K (peak in the microwave at 1.07 mm).
The CMB has a temperature of 2.725 K. Calculate its peak wavelength.
Solution. λ_max = 2.898 × 10⁻³ / 2.725 = 1.064 × 10⁻³ m ≈ 1.06 mm. This is in the microwave band — hence the name. The CMB satellites operate at frequencies of 30 – 900 GHz around this peak.
Estimate the redshift of the CMB photons by comparing their present temperature to the temperature at recombination (~3000 K).
Solution. Wavelength scales as 1/T for a black body (Wien), so 1 + z = T_emit / T_obs = 3000 / 2.725 = 1100. The CMB photons we observe today have been redshifted by a factor of about 1100 since they were emitted.
Between cosmic ages of about 3 minutes and 20 minutes (T ~ 10⁹ K), the temperature was right for fusion but the density was dropping rapidly with expansion. In this brief window, free protons and neutrons combined to form light nuclei: deuterium (²H), helium-3, helium-4, and trace amounts of lithium-7. Heavier elements could not be synthesised because the gap at mass-5 and mass-8 in the nuclear chart (no stable nuclei with those mass numbers) acted as a bottleneck — the chain stopped at helium.
The predicted mass fractions are:
These predictions, derived in the late 1940s by Gamow, Alpher and Herman, depend essentially on a single parameter — the baryon-to-photon ratio — and have been confirmed to high precision by observations of pristine intergalactic gas. The detailed agreement, especially the deuterium abundance, is one of the strongest pieces of evidence for the hot Big Bang.
Heavier elements (carbon, oxygen, iron, gold) were synthesised later, by stellar nucleosynthesis and supernova explosions — the chemistry of life is therefore a stellar inheritance.
graph TD
A["Big Bang model"] --> B["Hubble's Law<br/>v = H₀d<br/>(galaxies receding)"]
A --> C["Cosmic Microwave Background<br/>2.725 K black body<br/>(relic radiation)"]
A --> D["Primordial nucleosynthesis<br/>~75% H, ~25% He<br/>(matches predictions)"]
B --> E["Implies expansion;<br/>extrapolates to t ≈ 1/H₀"]
C --> F["Implies hot dense phase;<br/>recombination at z ≈ 1100"]
D --> G["Constrains baryon density<br/>and earliest minutes"]
Each pillar tests a different epoch of the standard model: Hubble's law tests the present, the CMB tests t = 380 000 years, primordial nucleosynthesis tests t = 3 minutes. Independent confirmation from three eras as different from each other as those is the strongest possible support a cosmological model could ask for.
The Big Bang model is enormously successful but leaves several major puzzles:
These are signposts for university-level study, not exam material.
Specimen question modelled on the AQA paper format.
(a) State Hubble's law and define each term. (3 marks)
(b) The Coma cluster of galaxies is observed to have a redshift z = 0.0231. Taking H₀ = 70 km s⁻¹ Mpc⁻¹, calculate (i) its recession velocity, (ii) its distance in Mpc, and (iii) its distance in m. (5 marks)
(c) Show that the Hubble time t_H = 1/H₀ has a value of approximately 1.4 × 10¹⁰ years using H₀ = 70 km s⁻¹ Mpc⁻¹. State the assumption made in interpreting this as the age of the universe. (4 marks)
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