Non-gaussianity for a Two Component Hybrid Model of Inflation

TL;DR

The paper analyzes a two-field hybrid inflation model with opposite-sign mass terms to evaluate non-Gaussianity via the Delta-N formalism. By deriving explicit expressions for the derivatives of the number of e-folds and the curvature perturbation, it computes the non-Gaussianity parameter f_NL and identifies parameter regimes where |f_NL| can reach O(1). The results indicate observable non-Gaussianity is possible only in a limited region, notably for a positive eta_sigma and negative eta_phi with specific initial field values, while many other parameter choices yield negligible f_NL. The work also assesses the spectral index, showing consistency with observational bounds in several regimes, and discusses the need for a physical motivation for large-field initial conditions in this framework.

Abstract

We consider a two component hybrid inflation model, in which two fields drive inflation. Our results show that this model generates an observable non-gaussian contribution to the curvature spectrum, within the limits allowed by the recent WMAP year 3 data. We show that if one field has a mass less than zero, and an initial field value less than 0.06Mpl while the other field has a mass greater than zero, and initial field value ranging between 0.5Mpl and Mpl then the non-gaussianity is observable with 1<fnl<1.5, but that fnl becomes much less than the observable limit should we take both masses to have the same sign, or if we loosened the constraints on the initial field values.

Figures (4)

• Figure 1: Contour plot of the absolute value of the maximum non-gaussianity generated for various combinations of masses, with initial conditions ranging between zero and the Planck mass. $|f_{\rm NL}|\gtrsim1$ corresponds to the four inner contours and the region outside the outermost contour corresponds to $|\frac{3}{5}f_{\rm NL}|_{max}<0.2$.
• Figure 2: Contour plot of the absolute value of the maximum non-gaussianity generated for various combinations of initial field values, with masses $\eta_{\phi}$ ranging between ($-0.04-0$) and $\eta_{\sigma}$ ranging between ($-0.04 - 0.15$). The embedded plot is a magnification of the region in which $|\frac{3}{5}f_{\rm NL}|>0.2$ appears, note that this corresponds to $\phi\ll1$ and $0.2\leq\sigma\leq1$.
• Figure 3: The potential Eq. (\ref{['pot']}) for $\eta_{\phi},\eta_{\sigma}>0$, in which the inflaton starts at a maximum and is pushed away from the origin by both fields. The solid black line corresponds to the unperturbed case $\sigma=0$
• Figure 4: The potential Eq. (\ref{['pot']}) for $\eta_{\phi}>0$ and $\eta_{\sigma}<0$, in which the $\phi$ field pushes the inflaton away from the origin while the $\sigma$ field pulls it $towards$ it. This case produces the more significant (yet still undetectable) values of $f_{\rm NL}$ which appear in Figs.\ref{['max']}&\ref{['contour_ini']}. The solid black line corresponds to the unperturbed case $\sigma=0$