Primordial non-gaussianities in general modified gravitational modelsof inflation

Abstract

We compute the three-point correlation function of primordial scalardensity perturbations in a general single-field inflationary scenario,where a scalar field ϕ has a direct coupling with the Ricci scalarR and the Gauss-Bonnet term \U0001d4a2.Our analysis also covers the models in which the Lagrangian includes afunction non-linear in the field kinetic energy X = −(∂ϕ)2/2,and a Galileon-type field self-interaction G(ϕ,X)□ϕ, where G is a function of ϕ and X. We provide a general analytic formula for the equilateral non-Gaussianity parameter fNLequil associated with the bispectrum of curvature perturbations.A quasi de Sitter approximation in terms of slow-variationparameters allows us to derive a simplified form of fNLequil 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-interactioncan 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), fNLequil is of the order of slow-roll parameters as in standard inflation driven by a minimally coupled scalar field.