Cosmological Implications of the PSCz PDF and its Moments

We compare the {\em pdf} and its low-order moments (variance and skewness) of the smoothed PSCz galaxy density field and of the corresponding simulated PSCz look-alikes, generated from N-body simulations of 6 different DM models; four structure normalized with $\Gamma=0.25$ and $\sigma_{8}=0.55 \Omega_{\circ}^{-0.6}$, one COBE normalized and the old SCDM. The galaxy distributions are smoothed with a Gaussian window at three different smoothing scales $R_{sm}=5$, 10 and $15 \hm$. We find that the simulation PSCz look-alike {\em pdf}'s are sensitive only on the normalization of the power spectrum, probably due to shape similarity of the simulated galaxy power spectrum on the relevant scales. We find that the only models that are consistent, at a high significance level, with the observed PSCz {\em pdf} are models with a relatively low power spectrum normalization $(\sigma_{8}=0.83)$. From the phenomenologically derived $\sigma_{8}-moments$ relation, fitted from the simulation data, we find that the PSCz moments suggest $\sigma_{8} \simeq 0.7$.