Best Unbiased Estimators for the Three-Point Correlators of the Cosmic Microwave Background Radiation

Abstract

Measuring the three-point correlators of the cosmic microwave background ~CMB! anisotropies could help to get a handle on the level of non-Gaussianity present in the observational data sets and therefore would strongly constrain models of the early Universe. However, typically, the expected non-Gaussian signal is very small. Therefore, one has to face the problem of extracting it from the noise, in particular from the ‘‘cosmic variance’’ noise. For this purpose, one has to construct the best unbiased estimators for the three-point correlators that are needed for concrete detection of non-Gaussian features. In this article, we study this problem for both the CMB third moment and the CMB angular bispectrum. We emphasize that knowledge of the best estimator for the former does not permit one to infer the best estimator for the latter and vice versa. We present the corresponding best unbiased estimators in both cases and compute their corresponding cosmic variances.