WHEN CAN NON-GAUSSIAN DENSITY FIELDS PRODUCE A GAUSSIAN SACHS-WOLFE EFFECT

The Sachs-Wolfe temperature fluctuations produced by primordial densit y perturbations are proportional to the potential field phi, which is a weighted integral over the density held delta. Because of the centra l limit theorem, phi can be approximately Gaussian even when delta is non-Gaussian. Using the Weld representation for non-Gaussian density f ields, delta(r) = integral f(\r-r'\)Delta(r')d(3)r', we find condition s on Delta and f for which phi must have a Gaussian one-point distribu tion, while delta can be non-Gaussian. Sufficient (but not necessary) conditions are that the density field have a power spectrum (which det ermines f) of P(k) proportional to k '', with -2<n less than or equal to+1, and that Delta(r) be non-Gaussian with no long-range correlation s. Thus there is an infinite set of non-Gaussian density fields which produce a nearly Gaussian one-point distribution for the Sachs-Wolfe e ffect.