Chapter 16

16. Cosmology & the Big Bang

College

The 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.

At a glance
Core ideaThe universe is expanding, and ran from a hot dense Big Bang 13.8 Gyr ago.
Key termHubble's Law — v = H₀d; farther galaxies recede faster.
You can…Estimate a galaxy's distance from its redshift velocity.
Watch outSpace itself stretches — this isn't galaxies flying through static space.
01 · Theory

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:

v = H0 d   H₀ ≈ 70 km/s/Mpc

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.

02 · Explanation

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.

Key ideaCosmological redshift is fundamentally different from a simple Doppler shift: it isn't caused by galaxies moving through space, but by space itself stretching while light travels across it — which is also why galaxies far enough away can recede faster than the speed of light without violating relativity; it is space, not matter, doing the "moving."
Early universe Today space expands Emitted (short λ) Observed (redshifted, long λ)
As space expands, galaxies spread apart and light travelling through it is stretched to longer, redder wavelengths.

A timeline of the universe

t = 0The Big BangThe universe begins in an extremely hot, dense state and starts expanding.
~1 secondFirst nucleiProtons and neutrons form; nucleosynthesis builds hydrogen and helium.
380,000 yrRecombination & the CMBAtoms form, the fog clears, and light streams free — the glow we still see.
~200 million yrFirst starsGravity gathers gas into the earliest stars and galaxies.
9.2 billion yrSolar System formsOur Sun and planets condense from a spinning nebula (4.6 Gyr ago).
13.8 billion yrTodayAn expanding, dark-energy-dominated universe — and you, reading this.
03 · Practical

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.

Solution
  1. Rearrange Hubble's Law: d = v / H0.
  2. Substitute: d = 7 000 / 70 = 100 Mpc.
  3. 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.

04 · Q&A

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.

Concept mind map

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.

Hubble's lawExpanding universeRecession velocityCMB afterglowBig Bang13.8 billion yrCosmology and the Big Bang
Infographic

The key facts, visualised

v = H0 d
Hubble's law: recession speed proportional to distance
~70 km/s/Mpc
Approximate value of the Hubble constant H0
13.8 billion yr
Age of the universe since the Big Bang
~2.7 K
Temperature of the cosmic microwave background today
Solved examples

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.

  1. v = H0 x d
  2. v = 70 x 100
  3. v = 7,000 km/s

Example 2A galaxy recedes at 14,000 km/s. Estimate its distance (H0 = 70 km/s/Mpc).

  1. d = v / H0
  2. d = 14,000 / 70
  3. d = 200 Mpc
Practice problem set

Now you try

Work each one out first, then tap to reveal the worked answer.

1State Hubble's law.
A galaxy's recession velocity is proportional to its distance: v = H0 d.
2What does the expansion of the universe imply about its past?
Everything was once much closer together in a hot, dense Big Bang.
3What is the cosmic microwave background?
The cooled afterglow of the early hot universe, now at about 2.7 K.
4Roughly how old is the universe?
About 13.8 billion years.
5What does the Hubble constant H0 measure?
The current expansion rate of the universe, about 70 km/s per Mpc.
6Does the CMB come from one direction or the whole sky?
From the whole sky; it fills all of space.