Non-Gaussianities from ekpyrotic collapse with multiple fields

TL;DR

The paper addresses non-Gaussianity in curvature perturbations produced during ekpyrotic collapse with multiple fields, using a two-field model with exponential potentials and the $\delta N$ formalism to track conversion of isocurvature to curvature perturbations at the transition to a single-field attractor. It shows that the resulting non-Gaussianity is local and, for realistic steep potentials, yields a large negative $f_{NL}$ via super-Hubble nonlinear evolution, with a blue spectrum for the curvature perturbation. This combination places strong observational constraints on the model, effectively ruling it out in its simplest form. The work clarifies the role of nonlinear, large-scale dynamics in multi-field ekpyrotic scenarios and informs viability considerations for related early-universe models.

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, $φ_1$ and $φ_2$, with exponential potentials, $-V_i \exp (-c_i φ_i)$, 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.

Figures (1)

• Figure 1: Left: An example of background solution for $\log \vert H \vert$ with initial condition $z=z_i$. We also show $\log \vert H_T \vert$ which is determined from the amplitude of $\delta \chi$. Right: The same background solution shown around $N \sim 0.01005$ which is much later than the transition. We also show the solutions with slightly different initial condition, $z=z_i + \delta z_i$, $z=z_i - \delta z_i$, with dashed lines. After the transition, this difference of initial $z$ generates the curvature perturbations which can be evaluated as the difference of $N$ at $H=H_f$.