  We present an approach to cosmological perturbations based on a covariant
perturbative expansion between two worldlines in the real inhomogeneous
universe. As an application, at an arbitrary order we define an exact scalar
quantity which describes the inhomogeneities in the number of e-folds on
uniform density hypersurfaces and which is conserved on all scales for a
barotropic ideal fluid. We derive a compact form for its conservation equation
at all orders and assign it a simple physical interpretation. To make a
comparison with the standard perturbation theory, we develop a method to
construct gauge-invariant quantities in a coordinate system at arbitrary order,
which we apply to derive the form of the n-th order perturbation in the number
of e-folds on uniform density hypersurfaces and its exact evolution equation.
On large scales, this provides the gauge-invariant expression for the curvature
perturbation on uniform density hypersurfaces and its evolution equation at any
order.
