Conservation of the nonlinear curvature perturbation in generic
  single-field inflation
  It is known that the curvature perturbation on uniform energy density (or
comoving or uniform Hubble) slices on superhorizon scales is conserved to full
nonlinear order if the pressure is only a function of the energy density (ie,
if the perturbation is purely adiabatic), independent of the gravitational
theory. Here we explicitly show that the same conservation holds for a universe
dominated by a single scalar field provided that the field is in an attractor
regime, for a very general class of scalar field theories. However, we also
show that if the scalar field equation contains a second time derivative of the
metric, as in the case of the Galileon theory, one has to invoke the
gravitational field equations to show the conservation.
