Conditions for large non-Gaussianity in two-field slow-roll inflation

TL;DR

Two-field slow-roll inflation can produce observable local non-Gaussianity $f_{NL}$ under specific separable-potential structures. The authors derive general conditions for large $f^{(4)}_{NL}$ in both product and sum potentials via the $ abla$delta N formalism and demonstrate explicit models achieving sizable non-Gaussianity, albeit requiring fine-tuned initial conditions. They show that introducing non-canonical kinetic terms can ease tuning, and they illustrate a hybrid inflation scenario with $f_{NL}$ around tens to fifty while keeping a nearly scale-invariant spectrum and small tensor-to-scalar ratio. The work highlights how the background trajectory evolution and the potential's shape govern the emergence of non-Gaussianity during inflation and notes caveats from loop corrections and quantum fluctuations that warrant further study.

Abstract

We study the level of primordial non-Gaussianity in slow-roll two-field inflation. Using an analytic formula for the nonlinear parameter f_nl in the case of a sum or product separable potential, we find that it is possible to generate significant non-Gaussianity even during slow-roll inflation with Gaussian perturbations at Hubble exit. In this paper we give the general conditions to obtain large non-Gaussianity and calculate the level of fine-tuning required to obtain this. We present explicit models in which the non-Gaussianity at the end of inflation can exceed the current observational bound of |f_nl|<100.

Figures (6)

• Figure 1: The contour plot of the functions, $f_p$, $g_p$ and $h_p$, in the plane of $\theta^*$, and $\theta^e$. The bottom and left-hand axes show the angles, $\theta^{*}$ and $\theta^{e}$ respectively. The top and right-hand axes show $\sin^{2}\theta^{*}$ and $\sin^{2}\theta^{e}$.
• Figure 2: A blown-up graph of Region B. The conditions for $g_p$ in Eqn. (\ref{['gen:Bconds']}) is plotted for ${\cal G}_p=1000$ with a white line. It can be seen that this condition encloses the contour for $g_p$ larger than some constant, ${\cal G}_p$.
• Figure 3: The contour plot of $\log_{10}| f^{(4)}_{\rm NL} |$ for Example A, $W(\varphi,\chi)=\frac{1}{2} e^{-\lambda\varphi^2/M_P^2} m^2\chi^2$. Here we used $\lambda=0.04$ (left) and $0.05$ (right). White regions indicate when $\vert f^{(4)}_{\rm NL} \vert<1$ and the dark centre-most region indicates $| f^{(4)}_{\rm NL} |>100$.
• Figure 4: The analytic evolution of $f^{(4)}_{\rm NL}$ and $\epsilon_\chi$ and $\epsilon_\varphi$ for Example A. The evolution of both fields, $\varphi$ and $\chi$ are also shown. We used $\lambda = 0.05$ and $\varphi_*=10^{-3}M_P$, $\chi_*= 16M_P$. We numerically solved the full equations of motion until $\epsilon=1$.
• Figure 5: The contour plot of $\log_{10}\vert f^{(4)}_{\rm NL} \vert$ with the sum potential, $W(\varphi,\chi)=V_0(1+\alpha\varphi^2+\beta\chi^2)$ (Example C). The parameters match the examples in Table \ref{['table_hybrid']} and the contours for $\log_{10}\vert f^{(4)}_{\rm NL} \vert$ are shown. White regions indicate when $\vert f^{(4)}_{\rm NL} \vert<1$.