Hubble's Law

The straight line v = H₀d is the observational core of the expanding universe: a galaxy twice as far recedes twice as fast. Lemaître derived it from general relativity in 1927; Hubble's 1929 plot of 24 galaxies made it an empirical fact, though his slope of ~500 km/(s·Mpc) was seven times too steep on a botched Cepheid calibration. The modern usage is mostly the middle rearrangement run in reverse: measure a redshift, divide by H₀, and out comes a distance — with H₀ = 70, a galaxy receding at 21 000 km/s sits 300 Mpc away, about a billion light-years.

H₀ is an input on this page rather than a baked-in constant, because its value is the sharpest open dispute in cosmology. Fitting the cosmic microwave background with the standard ΛCDM model gives 67.4 ± 0.5 km/(s·Mpc); climbing the local distance ladder of Cepheids and Type Ia supernovae gives 73.0 ± 1.0. The five-sigma gap — the "Hubble tension" — has survived a decade of cross-checks, so pick a side and enter it.

The constant's inverse is a clock. 1/H₀ has units of time, and at 67.4 km/(s·Mpc) works out to 14.5 billion years — the age the universe would have if it had always expanded at today's rate. The true age from the full expansion history is 13.8 billion years, close because the early deceleration and the late dark-energy acceleration nearly cancel. The same arithmetic sets the Hubble distance c/H₀ ≈ 4450 Mpc, the scale where the naive law extrapolates to lightspeed and redshift bookkeeping has to go properly relativistic.