Non-Gaussian Density Fluctuations from Entropically Generated Curvature Perturbations in Ekpyrotic Models

Abstract

We analyze the non-gaussian density perturbations generated in ekpyrotic/cyclic models based on heterotic M-theory. In this picture, two scalar fields produce nearly scale-invariant entropic perturbations during an ekpyrotic phase that are converted into curvature modes {\it after the ekpyrotic phase is complete} and just before the big bang. Both intrinsic non-linearity in the entropy perturbation and the conversion process contribute to non-gaussianity. The range of the non-gaussianity parameter $f_{NL}$ depends on how gradual the conversion process is and the steepness of the scalar field potential during the ekpyrotic phase. Although a wider range is possible, in principle, natural values of the ekpyrotic parameters combined with a gradual conversion process lead to values of $-60 \lesssim f_{NL} \lesssim +80$, typically much greater than slow-roll inflation but within the current observational bounds.