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 naïve notion of Euclidean distance at low redshift.

In 1929, Hubble accepted a finite expanding universe in order to explain the redshifts of distant galaxies, but soon relinquished that position as a consequence of observational constraints for a spatially infinite, non-expanding cosmological model. The authors show, by quoting his works, that he remained cautiously but steadfastly against the Big Bang version of events until the end of his life. His initial interpretation was that he was seeing in the apparent (but subsequently falsified) redshift-luminosity relationship in local galaxies the so-called “de Sitter effect", a representation of a materially scattering Universe.