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 after the ekpyrotic phase is complete and just before the big bang. Both intrinsic nonlinearity in the entropy perturbation and the conversion process contribute to non-Gaussianity. The range of the non-Gaussianity parameter ${f}_{\mathrm{NL}}$ 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 $\ensuremath{-}50\ensuremath{\lesssim}{f}_{\mathrm{NL}}\ensuremath{\lesssim}+200$, typically much greater than slow-roll inflation but within the current observational bounds.