Non--Gaussian Primordial Fluctuations

Abstract

We analyze the non--Gaussian primordial fluctuations which are inescapably contributed by scalar fields $\Phi$ with vanishing expectation values, $⟨\Phi ⟩=0$, present during inflation in addition to the inflaton field. For simplicity we take $\Phi$ to be non--interacting and minimally coupled to gravity. $\Phi$ is a Gaussian variable, but the energy density fluctuations contributed by such a field are ${\chi }^2$--distributed. We compute the three--point function $\xxxT$ for the configuration of an equilateral triangle (with side length $\ell$) and the skewness $\dddRR$, {\it i.e.} the third moment of the one--point probability distribution of the spatially smeared energy density contrast $\de_R$, where $R$ is the smearing scale. The relative magnitudes of the non--Gaussian effects, $[{\xi }^{(N)}{]}^{1/N}/[{\xi }^{(2)}{]}^{1/2}$, do not grow in time. They are given by numerical constants of order unity, independent of the scale $\ell$. The "bi--skewness" $\dddRS$ is positive. For smearing lengths $R\ll S$ this shows that in our model (in contrast to Gaussian models) voids are more quiet than high--density regions.

9 pages, uses AMSTex, 1 figure (not included)