Quadra-Spectrum and Quint-Spectrum from Inflation and Curvaton Models

TL;DR

This paper computes five- and six-point correlation functions of curvature perturbations in inflation and curvaton models, revealing how entropy perturbations and model specifics influence their magnitudes.

Contribution

It extends the calculation of higher-order spectra to multiple inflation models, including generalized kinetic terms and the curvaton scenario, highlighting conditions for their enhancement.

Findings

Quadra-spectrum and quint-spectrum are small in single-field slow-roll inflation.

Entropy perturbations can significantly boost these higher-order spectra.

In the curvaton model, these spectra are large when the tensor-to-scalar ratio is small.

Abstract

We calculate the quadra-spectrum and quint-spectrum, corresponding to five and six point correlation functions of the curvature perturbation. For single field inflation with standard kinetic term, the quadra-spectrum and quint-spectrum are small, which are suppressed by slow roll parameters. The calculation can be generalized to multiple fields. When there is no entropy perturbation, the quadra-spectrum and quint-spectrum are suppressed as well. With the presence of entropy perturbation, the quadra-spectrum and quint-spectrum can get boosted. We illustrate this boost in the multi-brid inflation model. For the curvaton scenario, the quadra-spectrum and quint-spectrum are also large in the small r limit. We also calculate representative terms of quadra-spectrum and quint-spectrum for inflation with generalized kinetic terms, and estimate their order of magnitude for quasi-single field inflation.