The Expanding Universe

Summary

We started from Module 2’s question — how far away is that object? — and finished at the expansion of the cosmos. The distance ladder climbs from parallax to standard candles to the Hubble flow, each rung calibrating the next. Hubble’s law, $v = H_0 d$, turns distance into recession speed, and inverting the expansion rate gives a first age of the universe, $1/H_0 \approx 14~\mathrm{Gyr}$. Cosmological redshift records the scale factor directly through $1+z = a_0/a$, and — pushed far enough — the same expansion carries distant galaxies apart faster than light, because space itself is stretching. Deep fields turn distance into lookback time, so the farthest galaxies show us the youngest universe.

We have measured how fast the universe expands, how far we can see, and roughly how old it is. The next question is what governs that expansion: what the universe is made of, and how its contents set its history. That is where we turn next.

Glossary

Cosmological redshift

Wavelength stretching caused by the expansion of the universe while light travels — distinct from an ordinary Doppler shift due to motion through space. It records the ratio of the present scale factor to the scale factor at emission.

Distance ladder

A chain of distance-measurement methods in which nearby calibrated methods support more distant methods — parallax calibrates Cepheids, Cepheids calibrate supernovae, and so on out to cosmological distances.

Hubble constant

The present-day expansion rate $H_0$ in Hubble’s law, usually written in $\mathrm{km\,s^{-1}\,Mpc^{-1}}$. Independent measurement chains currently disagree — early-universe methods give roughly $67$, local distance-ladder methods roughly $73$ — a gap called the Hubble tension, an active research frontier.

Hubble's law

The large-scale relation $v = H_0 d$, connecting galaxy recession speed and distance at low redshift. It is the empirical signature of cosmic expansion.

Lookback time

The time light has spent traveling from an object to us, so distant objects are seen as they were in the past. A deep field mixes many lookback times in one frame.

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.

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.

Standard candle

An object whose luminosity can be inferred — a Cepheid from its period, a Type Ia supernova from its light curve — allowing distance to be estimated from the observed flux via the inverse-square law.