Non--Gaussian Primordial Fluctuations

TL;DR

This paper investigates non-Gaussian primordial fluctuations from scalar fields during inflation, computing the three-point function and skewness, revealing scale-independent effects and that voids are quieter than high-density regions.

Contribution

It provides a detailed calculation of non-Gaussian effects from scalar fields with $ ext{chi}^2$-distributed energy density fluctuations during inflation, highlighting their scale independence.

Findings

Non-Gaussian effects are scale-independent and of order unity.

The bispectrum (three-point function) is computed for equilateral configurations.

Voids are found to be quieter than high-density regions in this model.

Abstract

We analyze the non--Gaussian primordial fluctuations which are inescapably contributed by scalar fields $\Phi$ with vanishing expectation values, $\langle\Phi\rangle=0$, 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.