Nflation: non-gaussianity in the horizon-crossing approximation

TL;DR

The paper investigates primordial non-Gaussianity in inflation models with multiple uncoupled fields and monomial potentials, using the horizon-crossing approximation and the $\delta N$ formalism. It derives an explicit, largely universal expression for $f_{\mathrm{NL}}$ when all fields share the same power $\alpha$, showing $-\frac{6}{5} f_{\mathrm{NL}} \simeq \frac{1}{2N}(2+f) = \frac{r}{8\alpha}(2+f)$, and extends the result to general $N_f$ and to differing $\alpha_i$ with slower convergence to an observable signal. The main finding is that $f_{\mathrm{NL}}$ is always slow-roll suppressed and too small to detect, even in multi-field scenarios, reinforcing the robustness of single-field-like predictions for $r$ and $n_s$ in these models. The work also highlights the possible role of post-inflationary mechanisms, such as curvatons, which are not considered here.

Abstract

We analyze the cosmic non-gaussianity produced in inflation models with multiple uncoupled fields with monomial potentials, such as Nflation. Using the horizon-crossing approximation to compute the non-gaussianity, we show that when each field has the same form of potential, the prediction is independent the number of fields, their initial conditions, and the spectrum of masses/couplings. It depends only on the number of e-foldings after the horizon crossing of observable perturbations. We also provide a further generalization to the case where the fields can have monomial potentials with different powers. Unless the horizon-crossing approximation is substantially violated, the predicted non-gaussianity is too small to ever be observed.