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

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.

18 pages; v2: Some equations and references are added; v3: Extended discussion on the relation among the Horndeski theory, the generalized Galileons, and the non-minimal coupling to the Gauss-Bonnet term: v4: final version accepted for publication in PTP