Non-Gaussianities from ekpyrotic collapse with multiple fields

TL;DR

This paper calculates the non-Gaussianity in curvature perturbations from ekpyrotic collapse with multiple fields, finding it to be large and incompatible with current observational constraints.

Contribution

It provides a detailed calculation of the bispectrum and non-Gaussianity parameter in a multi-field ekpyrotic model, linking theoretical predictions with observational limits.

Findings

Non-Gaussianity dominated by super-Hubble non-linear evolution

The non-linear parameter f_NL is proportional to the square of the potential exponent

The specific model is ruled out by current observational constraints

Abstract

We compute the non-Gaussianity of the curvature perturbation generated by ekpyrotic collapse with multiple fields. The transition from the multi-field scaling solution to a single-field dominated regime converts initial isocurvature field perturbations to an almost scale-invariant comoving curvature perturbation. In the specific model of two fields, $\phi_1$ and $\phi_2$, with exponential potentials, $-V_i \exp (-c_i \phi_i)$, we calculate the bispectrum of the resulting curvature perturbation. We find that the non-Gaussianity is dominated by non-linear evolution on super-Hubble scales and hence is of the local form. The non-linear parameter of the curvature perturbation is given by $f_{NL} = 5 c_j^2 /12$, where $c_j$ is the exponent of the potential for the field which becomes sub-dominant at late times. Since $c_j^2$ must be large, in order to generate an almost scale invariant spectrum, the non-Gaussianity is inevitably large. By combining the present observational constraints on $f_{\rm NL}$ and the scalar spectral index, the specific model studied in this paper is thus ruled out by current observational data.