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

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