16. Cosmology & the Big Bang
CollegeThe universe itself has a history — a beginning, an age, and an ongoing expansion — and the evidence for it is written in the sky in several independent ways.
Hubble's law and the expanding universe
In 1929, Edwin Hubble found that nearly every distant galaxy is redshifted, and more distant galaxies recede faster — a direct linear relationship known as Hubble's Law:
Crucially, this recession is not galaxies flying through static space — it is space itself expanding, stretching the wavelength of light travelling through it (cosmological redshift) and carrying galaxies apart with it. Running the expansion backward implies the universe began in an extremely hot, dense state roughly 13.8 billion years ago: the Big Bang.
The afterglow we can still see: the CMB
About 380,000 years after the Big Bang, the universe cooled enough for electrons and protons to combine into neutral hydrogen atoms (recombination), suddenly letting light travel freely for the first time. That light, phenomenally redshifted by 13.8 billion years of subsequent expansion, still fills the entire sky today as the Cosmic Microwave Background (CMB), a near-perfect blackbody glow at just 2.725 K — one of the strongest pieces of evidence for the Big Bang, discovered accidentally by Penzias and Wilson in 1965.
A timeline of the universe
Worked example — distance from Hubble's Law
A galaxy's spectrum shows it receding at v = 7 000 km/s. Using H0 = 70 km/s/Mpc, estimate its distance.
- Rearrange Hubble's Law: d = v / H0.
- Substitute: d = 7 000 / 70 = 100 Mpc.
- Convert megaparsecs to light-years (1 Mpc ≈ 3.26 million ly): d ≈ 100 × 3.26 million ≈ 326 million light-years.
Answer: about 100 megaparsecs, or roughly 326 million light-years away — and because the age of the universe is roughly 1/H0, this same relation, run in reverse, is also how Hubble's Law gives a rough estimate of the universe's age.
Test your understanding
What does Hubble's Law say, and what does it imply about the universe's history?
It says a galaxy's recession velocity is proportional to its distance from us. Run backward in time, this implies all galaxies were once much closer together, converging toward an extremely hot, dense state at a finite time in the past — the Big Bang, about 13.8 billion years ago.
What is the Cosmic Microwave Background, and why is it strong evidence for the Big Bang?
It is the redshifted afterglow of light released about 380,000 years after the Big Bang, when the universe first became transparent. Its near-perfect blackbody spectrum at 2.725 K, and its presence uniformly across the entire sky, matches precisely what Big Bang cosmology predicts and is difficult to explain any other way.
Is cosmological redshift the same thing as an ordinary Doppler shift?
Not exactly. An ordinary Doppler shift comes from a source physically moving through space. Cosmological redshift comes from space itself expanding while light travels through it, stretching the light's wavelength along the way — a distinct mechanism, though it produces a similar-looking reddening effect.
Why can distant galaxies appear to recede faster than the speed of light?
Because it is the space between us and them that is expanding, not the galaxies moving through space via ordinary motion. Special relativity's speed-of-light limit applies to motion through local space, not to the rate at which cosmic distances can grow due to the expansion of space itself.
How the ideas connect
Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.
The key facts, visualised
Worked problems, step by step
Follow each solution line by line, then try to reproduce it on paper before moving on.
Example 1A galaxy is 100 Mpc away. Using H0 = 70 km/s/Mpc, find its recession velocity.
- v = H0 x d
- v = 70 x 100
- v = 7,000 km/s
Example 2A galaxy recedes at 14,000 km/s. Estimate its distance (H0 = 70 km/s/Mpc).
- d = v / H0
- d = 14,000 / 70
- d = 200 Mpc
Now you try
Work each one out first, then tap to reveal the worked answer.