Editing Comoving and proper distances (section)

==Comoving coordinates==
Although [[general relativity]] allows the formulation of the laws of physics using arbitrary coordinates, some coordinate choices are easier to work with. Comoving coordinates are an example of such a coordinate choice. Conceptually each galaxy in the cosmos becomes a position on the coordinate axis. As the universe expands this position moves with the expansion.<ref name=Zee-2013>{{Cite book|url=https://www.worldcat.org/oclc/820123453|title=Einstein gravity in a nutshell|last=A.|first=Zee|date=5 May 2013|isbn=9780691145587|location=Princeton|oclc=820123453}}</ref>{{rp|290}} 

Comoving coordinates assign constant spatial coordinate values to observers who perceive the universe as [[Isotropy|isotropic]]. Such observers are called "comoving" observers because they move along with the [[Hubble's law|Hubble flow]]. The velocity of an object relative to the local comoving frame is called the [[peculiar velocity]] of that object. The peculiar velocity of a photon is always the [[speed of light]].<ref name=D&L_EC/>

Most large lumps of matter, such as galaxies, are nearly comoving, so that their peculiar velocities (owing to gravitational attraction) are small compared to their Hubble-flow velocity seen by observers in moderately nearby galaxies, (i.e. as seen from galaxies just outside the [[galaxy group|group]] local to the observed "lump of matter").

A comoving observer is the only observer who will perceive the universe, including the [[Cosmic microwave background|cosmic microwave background radiation]], to be isotropic. Non-comoving observers will see regions of the sky systematically [[blue-shift]]ed or [[red-shift]]ed. Thus isotropy, particularly isotropy of the cosmic microwave background radiation, defines a special local [[frame of reference]] called the [[Proper frame|comoving frame]].{{cn|date=May 2025}} 

In addition to position there is a '''comoving time''' coordinate,  the elapsed time since the [[Big Bang]] according to a clock of a comoving observer. The comoving spatial coordinates tell where an event occurs while this [[Cosmic time|cosmological time]] tells when an event occurs. Together, they form a complete [[coordinate system]], giving both the location and time of an event.

[[File:Kugelkoord-lokb-e.svg|thumb|A sphere with one radial coordinate and two angles.]]
A [[sphere|two-sphere]] drawn in 3D can be used to envision the concept of comoving coordinates. The surface of the sphere defines a two dimensional space that is homogeneous and isotropic. The two coordinates in the surface of the sphere are independent of the radius of the sphere: as the sphere expands these two coordinates are "comoving". If the radius expands over time  any tiny patch of the surface is unaffected but distant points on the sphere are physically further apart across the surface.<ref>{{Cite book |last=Kolb |first=Edward W. |title=The early universe |last2=Turner |first2=Michael S. |date=1994 |publisher=Addison-Wesley publ |isbn=978-0-201-11603-8 |series=Frontiers in physics |location=Redwood City (Calif.) Menlo Park (Calif.) Reading (Mass.) [etc.]}}</ref>{{rp|31}}