Primordial non-Gaussianities in general modified gravitational models of inflation

Details Primordial non-Gaussianities in general modified gravitational models of inflation Primordial non-Gaussianities in general modified gravitational models of inflation

2011-03-06

arxiv.org/abs/1103.1172v2

JCAP 1104:029,2011

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

25 pages, added subsection, uses RevTeX4-1

Scientific paper

10.1088/1475-7516/2011/04/029

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.

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