Correlation function (astronomy)

For other uses, see Correlation function (disambiguation).
Physical cosmology Universe · Big Bang
Age of the universe
Timeline of the Big Bang
Ultimate fate of the universeEarly universeExpanding universeComponentsIn astronomy, a correlation function describes the distribution of galaxies in the universe. By default, correlation function refers to the twopoint autocorrelation function. For a given distance, the twopoint autocorrelation function is a function of one variable (distance) which describes the probability that two galaxies are separated by this particular distance. It can be thought of as a lumpiness factor  the higher the value for some distance scale, the more lumpy the universe is at that distance scale.
The following definition (from Peebles 1980) is often cited:
 Given a random galaxy in a location, the correlation function describes the probability that another galaxy will be found within a given distance.
However, it can only be correct in the statistical sense that it is averaged over a large number of galaxies chosen as the first, random galaxy. If just one random galaxy is chosen, then the definition is no longer correct, firstly because it is meaningless to talk of just one "random" galaxy, and secondly because the function will vary wildly depending on which galaxy is chosen, in contradiction with its definition as a function.
The npoint autocorrelation functions for n greater than 2 or crosscorrelation functions for particular object types are defined similarly to the twopoint autocorrelation function.
The correlation function is important for theoretical models of physical cosmology because it provides a means of testing models which assume different things about the contents of the universe.
References
See also
 Correlation function in statistics
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