Multi-brid inflation and non-Gaussianity

Abstract

We consider a class of multi-component hybrid inflation models whose evolution may be analytically solved under the slow-roll approximation. We call it multi-brid inflation (or $n$-brid inflation where $n$ stands for the number of inflaton fields). As an explicit example, we consider a two-brid inflation model, in which the inflaton potentials are of exponential type and a waterfall field that terminates inflation has the standard quartic potential with two minima. Using the $δN$ formalism, we derive an expression for the curvature perturbation valid to full nonlinear order. Then we give an explicit expression for the curvature perturbation to second order in the inflaton perturbation. We find that the final form of the curvature perturbation depends crucially on how the inflation ends. Using this expression, we present closed analytical expressions for the spectrum of the curvature perturbation ${\cal P}_{S}(k)$, the spectral index $n_S$, the tensor to scalar ratio $r$, and the non-Gaussian parameter $f_{NL}^{\rm local}$, in terms of the model parameters. We find that a wide range of the parameter space $(n_S, r, f_{NL}^{\rm local})$ can be covered by varying the model parameters within a physically reasonable range. In particular, for plausible values of the model parameters, we may have large non-Gaussianity $f_{NL}^{\rm local}\sim 10$--100. This is in sharp contrast to the case of single-field hybrid inflation in which these parameters are tightly constrained.