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