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The proper distance provides a measurement of how far is a galaxy at a fixed moment in time. At the present time the proper distance equals the comoving distance since the cosmological scale factor has value one: $$a(t_0) = 1$$. The proper distance represents the distance obtained as if one were able to freeze the flow of time (set $$dt = 0$$ in the FLRW metric) and walk all the way to a galaxy while using a meter stick. For practical reason is calculated as the distance traveled by light (set $$ds = 0 $$ in the FLRW metric) from the time of emission by the galaxy to an observer (on Earth) at the present time. It differs form the light travel distance since the proper distance takes into account the expansion of the universe, i.e. the space expands as the light travels through it, resulting in numerical values which locate the most distant galaxies beyond the Hubble sphere and therefore with recessional velocities greater than the speed of light.

Most distant spectroscopically-confirmed objects
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