A general proof of the conservation of the curvature perturbation

Without invoking a perturbative expansion, we de. ne the cosmological curvature perturbation, and consider its behaviour assuming that the universe is smooth over a sufficiently large comoving scale. The equations are simple, resembling closely the first-order equations, and they lead to results which generalize those already proven in linear perturbation theory and ( in part) in second-order perturbation theory. In particular, the curvature perturbation is conserved provided that the pressure is a unique function of the energy density.