Cosmic Variance of the Three-Point Correlation Function of the Cosmic Microwave Background

Abstract

The fluctuations in the cosmic microwave background radiation may contain deviations from gaussian statistics which would be reflected in a nonzero value of three-point correlation function of $\Delta T$. However, any potential observation of the three-point function is limited by cosmic variance, even if a whole-sky map of $\Delta T$ is available. Here I derive a general formula for the cosmic variance of the three-point function in terms of integrals over the two-point function. This formula can be applied to any cosmological model and to any experimental measurement strategy. It gives a fundamental lower limit on the magnitude of a measurable three-point correlation function, and hence on the measurable amount of skewness in the distribution of $\Delta T$.