Contribution to the Three--Point Function of the Cosmic Microwave Background from the Rees--Sciama Effect

Abstract

We compute the contribution to the three--point temperature correlation function of the Cosmic Microwave Background coming from the non--linear evolution of Gaussian initial perturbations, as described by the Rees--Sciama (or integrated Sachs--Wolfe) effect. By expressing the collapsed three--point function in terms of multipole amplitudes, we are able to calculate its expectation value for any power spectrum and for any experimental setting on large angular scales. We also give an analytical expression for the {\it rms} collapsed three--point function arising from the cosmic variance of a Gaussian fluctuation field. In the case of {\it COBE} DMR, we find that the predicted signal is about three orders of magnitude below that expected from the cosmic variance.