Distance measures (cosmology)

Distance measures are used in physical cosmology to give a natural notion of the distance between two objects or events in the universe. They are often used to tie some observable quantity (such as the luminosity of a distant quasar, the redshift of a distant galaxy, or the angular size of the acoustic peaks in the CMB power spectrum) to another quantity that is not directly observable, but is more convenient for calculations (such as the comoving coordinates of the quasar, galaxy, etc.). The distance measures discussed here all reduce to the common notion of Euclidean distance at low redshift.

In accord with our present understanding of cosmology, these measures are calculated within the context of general relativity, where the Friedmann–Lemaître–Robertson–Walker solution is used to describe the universe.

There are a few different definitions of "distance" in cosmology which all coincide for sufficiently small redshifts. The expressions for these distances are most practical when written as functions of redshift ${\displaystyle z}$, since redshift is always the observable. They can easily be written as functions of scale factor ${\displaystyle a=1/(1+z)}$, cosmic ${\displaystyle t}$ or conformal time ${\displaystyle \eta }$ as well by performing a simple transformation of variables. By defining the dimensionless Hubble parameter and the Hubble distance ${\displaystyle d_{H}=c/H_{0}}$, the relation between the different distances becomes apparent.

...
Wikipedia