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The Expanding Universe

Section 2 of 6

Distance First, Then Expansion

Part 1: Distance First, Then Expansion

Imagine observing a galaxy spectrum and seeing that its lines are redshifted. That tells you the light has been stretched. But by itself, it does not yet tell you the expansion history of the universe. To discover a pattern, you need distances.

This is why the distance ladder matters. Nearby methods calibrate farther-reaching methods. Parallax calibrates local stars. Cepheids extend the ladder because their pulsation periods reveal their luminosities. Supernovae extend it farther still because they can be seen across enormous distances.

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.

Cepheid variable star light curve showing brightness rising and falling repeatedly over time, with points and a periodic curve overlaid on a star field.
Figure 1What to notice: Cepheids are useful because their brightness varies periodically. The period is the observable that calibrates their luminosity.ESO

A Cepheid’s brightness rises and falls in a regular pattern. The directly measured observable is time: the pulsation period. The model is the period-luminosity relation: longer-period Cepheids are more luminous. Once we know luminosity and measure flux, the inverse-square law gives distance.

Plot of Cepheid luminosity or magnitude versus pulsation period, showing a clear period-luminosity relation with example Cepheids.
Figure 2What to notice: longer-period Cepheids are more luminous. This relation turns a time measurement into a luminosity estimate, and luminosity plus flux gives distance.

This is a beautiful example of astronomical inference. A clock-like variation becomes a luminosity. A luminosity plus a flux becomes a distance. A distance plus a redshift becomes a point on the expansion diagram.

Supernova host galaxies help extend the same logic to larger distances. The important idea is not that every standard candle is identical in every detail. The important idea is calibration. Each rung works because a lower rung teaches us how to interpret a higher rung.

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.

Montage of galaxies that hosted supernovae, showing many galaxy images used for distance ladder and expansion measurements.
Figure 3What to notice: supernova host galaxies connect the local distance ladder to the Hubble flow. Standard candles let us compare distance and redshift far beyond the Milky Way.NASA/ESA/Hubble/Galaxy Zoo

Quick check

Why would redshifts alone not have been enough to discover Hubble’s law?