We define fully non-perturbative generalizations of the uniform density and
comoving curvature perturbations, which are known, in the linear theory, to be
conserved on sufficiently large scales for adiabatic perturbations. Our
non-linear generalizations are defined geometrically, independently of any
coordinate system. We give the equations governing their evolution on all
scales. Also, in order to make contact with previous works on first and second
order perturbations, we introduce a coordinate system and show that previous
results can be recovered, on large scales, in a remarkably simple way, after
restricting our definitions to first and second orders in a perturbative
expansion.Comment: 4 pages, version published in PRL 95, 091303 (2005