Non–Gaussian Primordial Fluctuations in Inflationary Cosmology

We analyze the non–Gaussian primordial fluctuations which are inescapably contributed by scalar fields Φ with vanishing expectation values, 〈Φ〉 = 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–distributed. We compute the three–point function ξ△ (l) for the configuration of an equilateral triangle (with side length l) and the skewness 〈δ3 R〉, i.e. the third moment of the one–point probability distribution of the spatially smeared energy density contrast δR, where R is the smearing scale. The relative magnitudes of the non–Gaussian effects, [ξ]/[ξ], do not grow in time. They are given by numerical constants of order unity, independent of the scale l. The ”bi–skewness” 〈δ2 RδS〉 is positive. For smearing lengths R ≪ S this shows that in our model (in contrast to Gaussian models) voids are more quiet than high–density regions. PACS numbers: 04.62.+v, 98.80.Cq, 98.65.Dx