Multi-brid inflation and non-Gaussianity

TL;DR

The paper develops a class of exactly solvable multi-component hybrid inflation models (multi-brid inflation) and uses the δN formalism to derive a fully nonlinear curvature perturbation. Focusing on a two-field realization with an exponential potential and a waterfall end, it provides closed-form expressions for the power spectrum, spectral index, tensor-to-scalar ratio, and local non-Gaussianity in terms of the model parameters. It finds n_S = 1 − (m_1^2 + m_2^2), describes r as a function of θ, γ, and coupling constants, and shows f_NL^{local} is nonnegative and can be large, mainly arising from the end-of-inflation surface. These results indicate that multi-field hybrids can yield a wide range of observable signatures, including sizable local non-Gaussianity, while potentially remaining consistent with WMAP/Planck constraints and offering connections to string-inspired inflation scenarios.

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.

Figures (2)

• Figure 1: A schematic diagram of classical trajectories in the field space with the coordinates $q^a$. The angular coordinates $n^a=q^a/q$ are conserved, and hence all the trajectories are radial in these coordinates. The curve indicated by $q=q_f$ denotes the surface at which the inflation ends, which may depends on $n^a$. The $e$-folding number $N$ is counted backward in time from $q=q_f$.
• Figure 2: Schematic graphs describing the three terms in Eq. (\ref{['dNlin']}). The thick lines represent three different kinds of orbits in the field space, and the thin lines with arrows on both ends represent the field fluctuations. The wavy dashed line represents the end of inflation. The one on the left corresponds to the first term, the one in the center to the second term, and the one on the right to the third term. See text for more details.