Scale factor

The scale factor is a dimensionless function of cosmic time that describes how distances between comoving points in the universe change as the universe expands or contracts.

Friedmann equations: Equations in general relativity that govern the expansion rate of a homogeneous, isotropic universe. They determine how the scale factor evolves from the universe’s contents and spatial curvature.
Friedmann–Lemaître–Robertson–Walker metric: A spacetime metric describing a homogeneous and isotropic universe. Its time-dependent spatial part contains the scale factor.
Redshift: The fractional increase in a wave’s wavelength between emission and observation. For cosmological sources, observed redshift gives the ratio of scale factors at observation and emission.
Hubble constant: The present-day value of the Hubble parameter, usually denoted H₀. It is the scale factor’s fractional growth rate today, not the scale factor itself.
Hubble parameter: The fractional rate of change of the scale factor with cosmic time. It is the scale factor’s instantaneous expansion rate, expressed as a rate per unit time.
Comoving coordinates: Coordinates that remain fixed for objects moving with the average cosmic expansion. They separate the universe’s changing size from the coordinate positions of distant matter.
Lookback time: The time elapsed between the emission of observed light and its detection. Its relation to redshift depends on the scale factor’s history.
Angular diameter distance: The ratio of an object’s physical transverse size to its observed angular size in cosmology. Its dependence on expansion and geometry prevents it from serving as a simple measure of cosmic size.
Cosmological redshift: The increase in photon wavelength caused by the expansion of the universe during a photon’s travel. A photon’s wavelength stretches in proportion to the scale factor’s growth.
Proper distance: The physical distance between locations measured on a spatial slice of spacetime. At a fixed cosmic time, proper distance scales with comoving separation times the scale factor.

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