Comoving distance

Comoving distance is a cosmological distance measure that remains fixed for objects moving with the expansion of the universe, separating that expansion from local motion.

Scale factor: A dimensionless measure of the universe’s relative size at a given cosmic time. Comoving coordinates stay fixed as this factor changes.
Proper distance: The physical separation between objects measured on a constant-time slice of spacetime. Unlike comoving distance, it changes as the universe expands.
Luminosity distance: The distance inferred from an object's intrinsic luminosity and observed flux. It predicts brightness, whereas comoving distance tracks expansion-factored separation.
Light-travel distance: The distance light travels over the elapsed time between emission and observation, expressed using that time interval. It measures elapsed photon travel rather than present comoving separation.
Hubble parameter: The rate of cosmic expansion at a specified time, expressed as the fractional growth rate of the scale factor. Its evolution sets how expansion accumulates along a light path.
Cosmological distance measures: A family of distance definitions used to relate cosmic observations to spatial separations and expansion. Comoving distance is one member of this set, with a distinct role in calculations.
Angular diameter distance: The distance relating an object's physical transverse size to its observed angular size. It governs apparent size and differs from comoving distance through cosmic expansion.
Hubble distance: The speed of light divided by the present Hubble parameter. It is a characteristic expansion scale, not the distance to a particular source.
Redshift: The increase in a photon’s wavelength as observed relative to its emitted wavelength. Observed redshift helps locate an object along the expanding universe’s history.
Cosmic time: Time measured by observers moving with the average expansion of a homogeneous universe. Distance comparisons depend on specifying the cosmic-time slices used to define them.

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