Evidence for Gaussian Initial Fluctuations from the 1.2 Jy IRAS Survey

We recover the one-point probability distribution function of the {\it initial} density fluctuations (\ipdf) from the quasi-linear galaxy density field of the 1.2 Jy \iras\ redshift survey smoothed by $10\hmpc$. The recovery, using the laminar, Eulerian, Zel'dovich approximation of Nusser and Dekel, is independent of $\Omega$ and is relatively insensitive to linear galaxy biasing in the range $0.5 \leq b \leq 2$. Errors due to discrete sampling, the limited survey volume, and the method of recovering the \ipdf\ are evaluated by comparing the \ipdf\ determined from the \iras\ data with Monte-Carlo \iras-like catalogs ``observed" from $N$-body simulations of CDM models with Gaussian initial conditions. Eight sensitive statistical tests used in this comparison find the \iras\ \ipdf\ to be consistent with Gaussian. We provide observational constraints on possible deviations from Gaussianity, which should be obeyed by any theoretical model.