Conservation of nonlinear curvature perturbations on super-Hubble scales

We consider general, non-linear curvature perturbations on scales greaterthan the Hubble horizon scale by invoking an expansion in spatial gradients,the so-called gradient expansion. After reviewing the basic properties of thegradient expansion, we derive the conservation law for non-linear curvatureperturbations for an isentropic fluid. We also define the gauge-invariantcurvature perturbation under a finite shift of time-slicing, and derive thenon-linear genralization of the $\delta N$ formalism. The results obtained arestraight-forward generalisations of those already proven in linear perturbationtheory, and the equations are simple, resembling closely the first-orderequations.Comment: 5 pages, 2 figures, to appear in the proceedings of PASCOS05, ed. by Kiwoon Choi, Jihn E. Kim and Dongchul Son, pub. by AI