![]() It is important to the definition of both comoving distance and proper distance in the cosmological sense (as opposed to proper length in special relativity) that all observers have the same cosmological age. Each observer measures their distance to the nearest observer in the chain, and the length of the chain, the sum of distances between nearby observers, is the total proper distance. All of these observers must have the same cosmological time. To measure the proper distance between two distant objects, one imagines that one has many comoving observers in a straight line between the two objects, so that all of the observers are close to each other, and form a chain between the two distant objects. Proper distance is also equal to the locally measured distance in the comoving frame for nearby objects. This is the same model as in the earlier figure, with dark energy and an event horizon.Ĭosmological time is identical to locally measured time for an observer at a fixed comoving spatial position, that is, in the local comoving frame. The x-axis is distance, in billions of light years the left-hand y-axis is time, in billions of years since the Big Bang the right-hand y-axis is the scale factor. The evolution of the universe and its horizons in proper distances. between two galaxies at time t is just the distance that would be measured by rulers between them at that time. as seen from galaxies just outside the group local to the observed "lump of matter").Ĭomoving coordinates separate the exactly proportional expansion in a Friedmannian universe in spatial comoving coordinates from the scale factor a ( t ). 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. The velocity of an observer relative to the local comoving frame is called the peculiar velocity of the observer. Thus isotropy, particularly isotropy of the cosmic microwave background radiation, defines a special local frame of reference called the comoving frame. Non-comoving observers will see regions of the sky systematically blue-shifted or red-shifted. ![]() Such observers are called "comoving" observers because they move along with the Hubble flow.Ī comoving observer is the only observer who will perceive the universe, including the cosmic microwave background radiation, to be isotropic. They assign constant spatial coordinate values to observers who perceive the universe as isotropic. ![]() Comoving coordinates are an example of such a natural coordinate choice. 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.Īlthough general relativity allows one to formulate the laws of physics using arbitrary coordinates, some coordinate choices are more natural or easier to work with. The evolution of the universe and its horizons in comoving distances.
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