Large non-Gaussianity from multi-brid inflation

TL;DR

This paper analyzes non-Gaussianity in a two-field hybrid inflation model (multi-brid inflation) with a quadratic-exponential potential and a generalized end-of-inflation ellipse. Using the $\delta N$ formalism, it derives analytic expressions for the curvature perturbation spectrum ${\cal P}_S$, spectral index $n_S$, tensor-to-scalar ratio $r$, and local non-Gaussianity $f_{NL}^{\rm local}$, highlighting how the end-surface geometry drives non-Gaussianities. In the equal-mass case, the authors show that large $f_{NL}^{\rm local}$ can be achieved simultaneously with a detectable $r$ by suitable parameter choices, and they provide explicit relations linking $r$ and $f_{NL}^{\rm local}$ to observations. They also analyze the large-mass-ratio limit, finding that while $f_{NL}^{\rm local}$ can be enhanced, $r$ remains constrained by the lighter field, making simultaneous observability unlikely. Overall, the study demonstrates that local non-Gaussianity can be large in multi-brid inflation and that end-of-inflation geometry plays a crucial role in determining observational signatures.

Abstract

A model of multi-component hybrid inflation, dubbed multi-brid inflation, in which various observable quantities including the non-Gaussianity parameter f_{NL} can be analytically calculated was proposed recently. In particular, for a two-brid inflation model with an exponential potential and the condition that the end of inflation is an ellipse in the field space, it was found that, while keeping the other observational quantities within the range consistent with observations, large non-Gaussianity is possible for certain inflationary trajectories, provided that the ratio of the two masses is large. One might question whether the resulting large non-Gaussianity is specific to this particular form of the potential and the condition for the end of inflation. In this paper, we consider a model of multi-brid inflation with a potential given by an exponential function of terms quadratic in the scalar field components. We also consider a more general class of ellipses for the end of inflation than those studied previously. Then, focusing on the case of two-brid inflation, we find that large non-Gaussianity is possible in the present model even for the equal-mass case. Then by tuning the model parameters, we find that there exist models for which both the non-Gaussianity and the tensor-to-scalar ratio are large enough to be detected in the very near future.

Figures (3)

• Figure 1: Definitions of parameters $\alpha$ and $\gamma$ in field space. The ellipse represents the surface of the end of inflation.
• Figure 2: Non-Gaussian parameter $f_{NL}^{\rm local}$ as a function of $\beta$ for several different values of $m^2$. The coupling constant parameters are set to $\lambda/g^4=1$. The spectral index is set to $n_S=0.96$. The curves are, from the one with the highest peak to that with the lowest peak, for $m^2=1/20$, $1/23$, $1/25$, $1/27$, and $1/30$.
• Figure 3: Tensor-to-scalar ratio $r$ as a functions of $\beta$ for several different values of $m^2$. The other parameters are the same as in Fig. \ref{['fig:fNL']}. The curves are, from the left to the right, for $m^2=1/20$, $1/23$, $1/25$, $1/27$, and $1/30$.