Hubble's Law: Reading the Expansion of the Universe Off a Straight Line

A straight line that rewrote cosmology

In 1929 Edwin Hubble plotted the recession velocity of distant galaxies (measured from their redshift) against their distance (estimated from Cepheid variable stars) and found, roughly, a straight line through the origin: v = H₀·d. Velocity increases directly with distance — a galaxy twice as far recedes roughly twice as fast. The constant of proportionality, H₀, the Hubble constant, is usually quoted in km/s per megaparsec; modern measurements cluster around 67-73 km/s/Mpc, and the small but persistent gap between different measurement methods is an active area of research known as the Hubble tension.

Redshift is not a Doppler shift, exactly

It is tempting to read the recession as galaxies physically flying away from us through static space, exactly like a receding ambulance's siren dropping in pitch. General relativity gives a subtly different picture: space itself is expanding, stretching the wavelength of light in transit — cosmological redshift — rather than the galaxy moving through fixed space. At low redshift the two pictures give nearly identical numbers, which is why the Doppler analogy survives in casual explanation, but at higher redshift only the expanding-space picture stays consistent with observation, and it is the one that lets galaxies recede faster than light without violating relativity: no galaxy is moving faster than light through local space, the space between us and it is simply growing.

Hubble's law:                v = H0 * d
redshift-velocity (v << c): z ~ v / c
Hubble time (age proxy):     t_H = 1 / H0  ~  13.8 Gyr for H0 ~ 70 km/s/Mpc

The Hubble constant is not actually constant

Despite the name, H₀ changes over cosmic history — it is the expansion rate today, and the more general Hubble parameter H(t) evolves as the universe's contents change. Early on, radiation and matter dominated and their gravity decelerated the expansion; roughly the last five billion years have been dominated by dark energy, whose repulsive effect is now accelerating the expansion rate again. That handoff — deceleration giving way to acceleration — was discovered from distant Type Ia supernovae appearing fainter (further away) than a matter-only universe would predict, work that won the 2011 Nobel Prize in Physics.

Distance, velocity and the edge of what we can see

Because v = H₀·d has no upper limit built in, sufficiently distant galaxies recede faster than light — not a contradiction, since it is the space between us that is stretching rather than any object moving locally faster than light through it. This defines a real horizon: the observable universe, roughly 46.5 billion light-years in radius today, is the region from which light has had time to reach us since the Big Bang, folded together with almost 13.8 billion years of subsequent expansion stretching that original distance further still. Galaxies beyond the horizon are not gone, they are simply not yet — and in an accelerating universe, may never be — reachable by any signal we send.

Measuring H0: two methods, one persistent disagreement

The local ladder method builds distances step by step through the nearby universe — parallax to Cepheid variables, then Cepheids to calibrate Type Ia supernovae, then supernovae out to hundreds of megaparsecs — and currently gives H₀ ≈ 73 km/s/Mpc. The early universe method instead fits the full cosmological model (matter, radiation, dark energy densities) to the fine temperature pattern of the cosmic microwave background left over from 380,000 years after the Big Bang, and extrapolates H₀ forward through that model to today, giving ≈ 67 km/s/Mpc. The two methods disagree by about 8%, far more than their stated uncertainties allow — the Hubble tension — and whether it points to new physics in the early universe or an unrecognised systematic error in one of the ladders is still unresolved.

Frequently asked questions

Try it live

Everything above runs in your browser — open Hubble's Law and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.