Generalized G-inflation: Inflation with the most general second-order field equations

TL;DR

This paper introduces Generalized G-inflation, a comprehensive framework for single-field inflation models that encompasses previous models and provides the most general second-order field equations, analyzing stability and primordial fluctuations.

Contribution

It develops the most general single-field inflation model framework, Generalized G-inflation, including stability analysis and perturbation spectra, unifying various previous models under one theory.

Findings

Derived the most general quadratic actions for perturbations.

Established the equivalence between Horndeski theory and generalized Galileons.

Included non-minimal couplings like Gauss-Bonnet in the framework.

Abstract

We study generalized Galileons as a framework to develop the most general single-field inflation models ever, Generalized G-inflation, containing yet further generalization of G-inflation, as well as previous examples such as k-inflation, extended inflation, and new Higgs inflation as special cases. We investigate the background and perturbation evolution in this model, calculating the most general quadratic actions for tensor and scalar cosmological perturbations to give the stability criteria and the power spectra of primordial fluctuations. It is pointed out in the Appendix that the Horndeski theory and the generalized Galileons are equivalent. In particular, even the non-minimal coupling to the Gauss-Bonnet term is included in the generalized Galileons in a non-trivial manner.