Conservation of the nonlinear curvature perturbation in generic single-field inflation

Abstract: 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.