Cosmological redshift

Cosmological redshift is the lengthening of the wavelength of light as it travels through an expanding universe. It is quantified by the redshift z, defined through 1 + z = lambda_observed / lambda_emitted. In an expanding Friedmann-Lemaitre-Robertson-Walker universe this ratio equals the ratio of the scale factor now to the scale factor at emission: 1 + z = a(now) / a(emit). A galaxy observed at z = 1 emitted its light when the universe was half its present size; its light has been stretched to twice the original wavelength. Because the relation involves only the scale factor, the redshift is a direct measurement of how much the universe has expanded since the light was emitted.

Despite its appearance, cosmological redshift is not a Doppler shift. A Doppler shift arises from a source moving through space relative to the observer; cosmological redshift arises because the space between source and observer itself expands, stretching the wave that travels through it. The two coincide only at low redshift, where z is approximately equal to v/c and the local Hubble law v = H_0 d can be read either way. At large redshift they diverge sharply: the naive 'redshift velocity' cz exceeds the speed of light for z greater than one, which is meaningless as a velocity but perfectly sensible as a statement about the scale factor. Comoving galaxies can have recession velocities greater than c without violating relativity, because no object is moving through space.

Cosmological redshift is the principal tool of observational cosmology. It serves as a clock and a ruler: each redshift corresponds, through the Friedmann equations, to a definite age of the universe at emission and a definite scale factor. The cosmic microwave background arrives at z is approximately 1100, telling us the universe has expanded by a factor of 1101 and was about 380,000 years old when that light was released. Quasars, supernovae, and galaxies at intermediate redshifts let astronomers reconstruct the entire expansion history and infer the matter and dark-energy content of the universe.

Vesto Slipher measured the first nebular redshifts at the Lowell Observatory between 1912 and 1917, finding most spiral nebulae receding. Hubble's 1929 velocity-distance relation interpreted these shifts as proportional to distance. The relativistic interpretation — wavelengths stretching with the scale factor rather than a Doppler effect — was developed by Georges Lemaitre (1927) and Howard Robertson within the FLRW framework, distinguishing cosmological redshift from kinematic Doppler shift.