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

TL;DR

The paper establishes Generalized G-inflation within the generalized Galileon/Horndeski framework, deriving the most general second-order single-field inflation model and its full background and perturbation dynamics. It introduces a Lagrangian with four φ,X-dependent functions K, G_3, G_4, G_5, demonstrates Horndeski equivalence, and shows how non-minimal Gauss-Bonnet couplings are embedded. The authors derive the general quadratic actions for tensor and scalar perturbations, specify the stability conditions via 𝓕_T, 𝔊_T, 𝓕_S, and 𝔊_S, and provide expressions for the power spectra and tensor-to-scalar ratio, including the possibility of a blue tensor spectrum and new consistency relations in slow-roll regimes. These results unify and extend known models such as k-inflation and Higgs inflation, offering a robust foundation for exploring non-Gaussianities and broader observational consequences. The framework naturally accommodates a broad class of inflationary dynamics and enables systematic comparison with observations and fundamental theories.

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.