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Using the tool of Hodge-Morrey decomposition of forms, we prove a newdecomposition of symmetric rank-2 tensors on Ricci flat manifolds withboundary. Using this we reconstruct a new cosmological perturbation theory thatallows for the scalar-vector-tensor type separation of the linearized Einsteinequations with general boundary conditions. We discuss gauge transformations,gauge invariant quantities and as an example how the new decomposition worksout in the single-field inflation scenario. For the scalar modes we get twocopies of Mukhanov-Sasaki equation, one of them with a slight modification.Additionally we run a Weinberg-like argument for the existence adiabatic modes,and find some gauge-invariant solutions to the perturbations that existswhatever the constituents of the universe are.

Cosmological perturbations out of the box I