### Abstract

We compute the three-point correlation function of primordial scalar density perturbations in a general single-field inflationary scenario, where a scalar field φ has a direct coupling with the Ricci scalar R and the Gauss-Bonnet term . Our analysis also covers the models in which the Lagrangian includes a function 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 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.

Original language | English |
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Article number | 029 |

Journal | Journal of Cosmology and Astroparticle Physics |

Volume | 2011 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2011 Apr |

Externally published | Yes |

### Keywords

- cosmological perturbation theory
- inflation
- non-gaussianity

### ASJC Scopus subject areas

- Astronomy and Astrophysics