Primordial non-Gaussianities in general modified gravitational models of inflation

TL;DR

This work derives the full bispectrum for a broad class of single-field inflationary models that include nonminimal curvature coupling $F(\phi)R$, Gauss-Bonnet coupling $\xi(\phi){\cal G}$, and noncanonical kinetic/Galileon terms $P(\phi,X)$ and $G(\phi,X)\Box\phi$. Using the ADM-based perturbation theory, it obtains the second- and third-order actions for the curvature perturbation, yielding a general analytic expression for the equilateral non-Gaussianity parameter $f_{NL}^{equil}$ in quasi-de Sitter backgrounds and a slow-variation expansion that isolates the leading contributions. The results show that a small scalar sound speed $c_s$ can generate large non-Gaussianities via Gauss-Bonnet and Galileon terms, while Brans-Dicke and $f(R)$-type theories predict $f_{NL}^{equil}$ of order slow-roll parameters. The paper provides concrete predictions for k-inflation, generalized Galileon, and Brans-Dicke/GB-influenced models, enabling observational constraints from Planck-like data on the inflationary model space.

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.