Intuitive understanding of non-Gaussianity in ekpyrotic and cyclic models

Abstract

It has been pointed out by several groups that ekpyrotic and cyclic models generate significant non-Gaussianity. In this paper, we present a physically intuitive, semianalytic estimate of the bispectrum. We show that, in all such models, there is an intrinsic contribution to the non-Gaussianity parameter ${f}_{NL}$ that is determined by the geometric mean of the equation of state ${w}_{ek}$ during the ekpyrotic phase and ${w}_{c}$ during the phase that curvature perturbations are generated, and whose value is $\mathcal{O}(100)$ or more times the intrinsic value predicted by simple slow-roll inflationary models, ${f}_{NL}^{\mathrm{intrinsic}}=\mathcal{O}(0.1)$. Other contributions to ${f}_{NL}$, which we also estimate, can increase $|{f}_{NL}|$ but are unlikely to decrease it significantly, making non-Gaussianity a useful test of these models. Furthermore, we discuss a predicted correlation between the non-Gaussianity and scalar spectral index that sharpens the test.