Editing Comoving and proper distances (section)

==Comoving coordinates==
[[File:Spacetime-diagram-flat-universe-comoving-coordinates.png|thumb|left|upright=1.2|alt=comoving coordinates|The evolution of the universe and its horizons in comoving distances. The x-axis is distance, in billions of light years; the y-axis is time, in billions of years since the Big Bang. This model of the universe includes dark energy which causes an accelerating expansion after a certain point in time, and results in an [[event horizon]] beyond which we can never see.]]

Although [[general relativity]] allows the formulation of the laws of physics using arbitrary coordinates, some coordinate choices are more natural or easier to work with. Comoving coordinates are an example of such a natural coordinate choice. They 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]].
<!-- was: a scientist to [[Formula|formulate]] the laws of physics using an arbitrary system of [[coordinates]], a scientist's job can be simplified by using different coordinate systems that are easy to work with. -->

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]]. The velocity of an observer relative to the local comoving frame is called the [[peculiar velocity]] of the observer.

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").

[[File:Cosmos-animation Lambda-CDM.gif|thumb|right|upright=1.6|alt=comoving coordinates|Comoving coordinates separate the exactly proportional expansion in a Friedmannian universe in spatial comoving coordinates from the scale factor <math>a(t)~.</math> This example is for the &Lambda;CDM model.]]
The '''comoving time''' coordinate is the elapsed time since the [[Big Bang]] according to a clock of a comoving observer and is a measure of [[Cosmic time|cosmological time]]. The comoving spatial coordinates tell where an event occurs while cosmological time tells when an event occurs. Together, they form a complete [[coordinate system]], giving both the location and time of an event.

Space in comoving coordinates is usually referred to as being "static", as most bodies on the scale of galaxies or larger are approximately comoving, and comoving bodies have static, unchanging comoving coordinates. So for a given pair of comoving galaxies, while the proper distance between them would have been smaller in the past and will become larger in the future due to the expansion of the universe, the comoving distance between them remains ''constant'' at all times.

The expanding Universe has an increasing [[Scale factor (cosmology)|scale factor]] which explains how constant comoving distances are reconciled with proper distances that increase with time.