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:

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.

The standard big bang model is usually supplemented with cosmic inflation. In inflationary models, the observer only sees a tiny fraction of the whole universe, much less than a billionth (1/10⁹) of the volume of the universe postulated in inflation. So the observable universe (the so-called particle horizon of the universe) is the result of processes that follow some general physical laws, including quantum mechanics and general relativity. Some of these processes are random: for example, the distribution of galaxies throughout the universe can only be described statistically and cannot be derived from first principles.

This raises philosophical problems: suppose that random physical processes happen on length scales both smaller than and bigger than the horizon. A physical process (such as an amplitude of a primordial in density) that happens on the horizon scale only gives us one observable realization. A physical process on a larger scale gives us zero observable realizations. A physical process on a slightly smaller scale gives us a small number of realizations.

In the case of only one realization it is difficult to draw statistical conclusions about its significance. For example, if the underlying model of a physical process implies that the observed property should occur only 1% of the time, does that really mean that the model is excluded? Consider the physical model of the citizenship of human beings in the early 21st century, where about 30% are Indian and Chinese citizens, about 5% are American citizens, about 1% are French citizens, and so on. For an observer who has only one observation (of his/her own citizenship) and who happens to be French and cannot make any external observations, the model can be rejected at the 99% significance level. Yet the external observers with more information unavailable to the first observer, know that the model is correct.

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