Large non-Gaussianity from two-component hybrid inflation

Abstract

We study the generation of non-Gaussianity in models of hybrid inflation with two inflaton fields, (2-brid inflation). We analyse the region in the parameter and the initial condition space where a large non-Gaussianity may be generated during slow-roll inflation which is generally characterised by a large f_NL, tau_NL and a small g_NL. For certain parameter values we can satisfy tau_NL>>f_NL^2. The bispectrum is of the local type but may have a significant scale dependence. We show that the loop corrections to the power spectrum and bispectrum are suppressed during inflation, if one assume that the fields follow a classical background trajectory. We also include the effect of the waterfall field, which can lead to a significant change in the observables after the waterfall field is destabilised, depending on the couplings between the waterfall and inflaton fields.

Figures (4)

• Figure 1: Left: The contour plot of $f_{\rm NL}$ which have the end condition same as uniform energy density hypersurface $g_1^2/g_2^2=\eta_{\varphi\varphi}/\eta_{\chi\chi}$ in \ref{['subsecA']} in the plane of phi and chi, which denote the values of the fields when the given scale leaves the horizon. The values of $f_{\rm NL}$, 0, 10 and 20, are shown on the corresponding contour. For example with the given end point, the trajectory is shown as a line denoted by "Traj". The cross point with $N_k=60$ line is the value of phi and chi when the scale corresponding to $N_k=60$ leaves horizon. In this scale the value of $f_{\rm NL}$ is around 9. Right: Directly from the left figure, we can read the scale dependence of $f_{\rm NL}$ on the given trajectory. For the given trajectory the spectrum of $f_{\rm NL}$ is shown in the figure. For this trajectory we used the third example in Table \ref{['table_hybrid']}, i.e. $\eta_{\varphi\varphi}=0.08$, $\eta_{\chi\chi}=0.01$, and the end point is fixed so that the field values $\varphi_*=1$ and $\chi_*=0.0018$ lead to the number of e-foldings $N_k=60$.
• Figure 2: Same as Fig. \ref{['hybridA']} but using the end condition $g_1^2=g_2^2$, see \ref{['subsecB']}.
• Figure 3: Tree level diagrams for the power spectrum (left hand side), the bispectrum (centre) and the relevant tree diagram for the trispectrum (right) which corresponds to $\tau_{NL}$. The diagrams were drawn using JAXODRAW Binosi:2003yf
• Figure 4: The dominant one-loop level diagrams for the power spectrum (left hand side), the bispectrum (centre) and the trispectrum (right).