The Expanding Universe

Section 1 of 6

Concept Throughline

By the end of this reading, you will be able to:

Explain
why redshift alone is not enough — cosmology needs distances too
Trace
the completed distance ladder, from parallax to standard candles to the Hubble flow
Use
Hubble’s law $v = H_0 d$ to find a recession speed, and $1/H_0$ to estimate the age of the universe
Distinguish
cosmological redshift from ordinary Doppler motion, reading it as the scale-factor stretch
Explain
why recession faster than light is allowed, and why $v = H_0 d$ is a low-redshift law
Use
deep fields as evidence that looking far away means looking back in time

Concept Throughline

The universe is not simply a stage where galaxies move. The stage itself changes. Light crossing that changing stage carries a record of how far, how fast, and how long ago.

This reading takes up the question Module 2 opened with — how far away is that object? — and follows it all the way to the edge of the observable universe. The method is unchanged: observe → model → infer. We observe redshifts and standard-candle brightnesses. We model light crossing expanding spacetime. Then we infer distances, the expansion rate, and a first estimate of the age of the universe.

The surprise is what the model demands. When we extend the simple law that organizes the data, it predicts galaxies receding faster than light — and that turns out to be allowed, because it is space itself that expands.

Observable

Redshift and standard-candle brightness

A galaxy’s spectral lines arrive stretched toward longer wavelengths, and a standard candle inside it (a Cepheid, a Type Ia supernova) arrives at a measurable brightness.

Model

Light crossing expanding spacetime

The brightness gives distance through the inverse-square law; the stretch gives the scale factor through $1+z = a_0/a_\text{emit}$ ; and on large scales the two are tied by Hubble’s law, $v = H_0 d$ .

Inference

Distance, expansion rate, and a first age

Together they fix how far the galaxy is, how fast the space between us is stretching, and — by inverting the expansion rate — roughly how long the universe has been expanding.

Spacetime

The combined description of space and time. In cosmology, expanding spacetime means the scale factor changes with time, stretching large-scale distances and the wavelengths of traveling light.

Scale factor

A quantity, written $a(t)$ , that describes the relative size of the universe at a given cosmic time. Normalizing today to $a_0 = 1$ , a past epoch with $a = 1/2$ is when the universe was half its present scale.