Inflation and primordial non-Gaussianities of "generalized Galileons"

TL;DR

The work tackles primordial perturbations in the most general second-derivative scalar-tensor theory known as the generalized Galileon, encompassing k-inflation and G-inflation as limits. It develops a complete perturbation framework up to cubic order, deriving the background equations, linear perturbations, and the full third-order action for the curvature perturbation. The key findings are a modified tensor-to-scalar ratio and propagation speeds in the scalar and tensor sectors, and a bispectrum whose shapes do not introduce new momentum configurations beyond those in k-inflation, with an explicit equilateral f_NL expression. This formalism enables broad observational constraints on the free functions K and G^(n) and their impact on early-Universe dynamics.

Abstract

We set up cosmological perturbation theory and study the cosmological implications of the so-called ``generalized Galileon'' developed in \cite{Deffayet:2011gz,horndeski}. This is the most general scalar field theory whose Lagrangian contains derivatives up to second order while keeping second order equations of motion, and contains as sub-cases $k$-inflation, $G$-inflation and many other models. We calculate the power spectrum of the primordial curvature perturbation, finding a modification of the usual consistency relation of the tensor-to-scalar ratio in $k$-inflation or perfect fluid models. Finally we also calculate the bispectrum, which contains no new shapes beyond those of $k$-inflation.