Cosmic Variance

The term Cosmic variance is the statistical uncertainty inherent in observations of the universe at extreme distances. It has three different but closely related meanings:

• It is sometimes used, incorrectly, to mean sample variance - the difference between different finite samples of the same parent population. Such differences follow a Poissonian distribution, and in this case the term sample variance should be used instead.
• It is sometimes used, mainly by cosmologists, to mean the uncertainty due to the fact that that we can only observe one realization of all the possible observable universes. For example, we can only observe one Cosmic Microwave Background, so the measured positions of the peaks in the Cosmic Microwave Background spectrum, integrated over the visible sky, are limited by the fact that only one spectrum is observable from Earth. The observable Universe viewed from another Galaxy will have the peaks in slightly different places, while remaining consistent with the same physical laws, inflation, etc. This second meaning may be regarded as a special case of the third meaning.
• The most widespread use, to which the rest of this article refers, reflects the fact that measurements are affected by cosmic large-scale structure, so a measurement of any region of sky (viewed from Earth) may differ from a a measurement of a different region of sky (also viewed from Earth) by an amount that may be much greater than the sample variance.

This most widespread use of the term is based on the idea that it is only possible to observe part of the universe at one particular time, so it is difficult to make statistical statements about cosmology on the scale of the entire universe, as the number of observations (sample size) must be too small.