Non--Gaussian Primordial Fluctuations

Abstract

We analyze the non--Gaussian primordial fluctuations which are inescapably contributed by scalar fields $Φ$ with vanishing expectation values, $\langleΦ\rangle=0$, present during inflation in addition to the inflaton field. For simplicity we take $Φ$ to be non--interacting and minimally coupled to gravity. $Φ$ is a Gaussian variable, but the energy density fluctuations contributed by such a field are $χ^2$--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, $[ξ^{(N)}]^{1/N}/[ξ^{(2)}]^{1/2}$, 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.