Non-Gaussian CMBR angular power spectra

Abstract

In this paper we show how the prediction of CMBR angular power spectra ${\mathit{C}}_{\mathit{l}}$ in non-Gaussian theories is affected by a cosmic covariance problem; that is, (${\mathit{C}}_{\mathit{l}}$,${\mathit{C}}_{\mathit{l}\ensuremath{'}}$) correlations impart features on any observed ${\mathit{C}}_{\mathit{l}}$ spectrum which are absent from the average ${\mathit{C}}^{\mathit{l}}$ spectrum. Therefore the average spectrum is rendered a bad observational prediction, and two new prediction strategies, better adjusted to these theories, are proposed. In one we search for hidden random indices conditional to which the theory is released from the correlations. Contact with experiment can then be made in the form of the conditional power spectra plus the random index distribution. In another approach we apply to the problem a principal component analysis. We discuss the effect of correlations on the predictivity of non-Gaussian theories. We finish by showing how correlations may be crucial in delineating the borderline between predictions made by non-Gaussian and Gaussian theories. In fact, in some particular theories, correlations may act as powerful non-Gaussianity indicators.