Primordial non-Gaussianities in general modified gravitational models of inflation

TL;DR

This paper derives a general formula for primordial non-Gaussianities in a wide class of inflation models with scalar fields coupled to curvature terms, providing tools to constrain these models with future observations.

Contribution

It presents a unified analytic expression for the equilateral non-Gaussianity parameter in diverse modified gravity inflation scenarios, including non-linear kinetic terms and Galileon interactions.

Findings

Large non-Gaussianities possible with small scalar propagation speed.

In Brans-Dicke and f(R) models, non-Gaussianity remains small, similar to standard inflation.

The formula facilitates observational constraints on complex inflation models.

Abstract

We compute the three-point correlation function of primordial scalar density perturbations in a general single-field inflationary scenario, where a scalar field phi has a direct coupling with the Ricci scalar R and the Gauss-Bonnet term GB. Our analysis also covers the models in which the Lagrangian includes a function non-linear in the field kinetic energy X=-(nabla phi)^2/2, and a Galileon-type field self-interaction G(phi, X)*(Box phi), where G is a function of phi and X. We provide a general analytic formula for the equilateral non-Gaussianity parameter f_{NL}^{equil} associated with the bispectrum of curvature perturbations. A quasi de Sitter approximation in terms of slow-variation parameters allows us to derive a simplified form of f_{NL}^{equil} convenient to constrain various inflation models observationally. If the propagation speed of the scalar perturbations is much smaller than the speed of light, the Gauss-Bonnet term as well as the Galileon-type field self-interaction can give rise to large non-Gaussianities testable in future observations. We also show that, in Brans-Dicke theory with a field potential (including f(R) gravity), f_{NL}^{equil} is of the order of slow-roll parameters as in standard inflation driven by a minimally coupled scalar field.