A quantum theory of cosmological perturbations is based on the action of Einstein gravity with matter expanded io quadratic order around a background solution of the field equations. If, in the Schriidinger picture, the wavefunction is assumed lo factorize such that each faclor is a function of only a finite number of degrees of freedom (e.g. Fourier wmponenls of the fields) all gauge constrain& can be solved explicitly. This generalizes previous gaugehvarianl quantizarions while clarifying their Limited soape. The result is cast into the more wnvenient Heisenberg picture. It can be found directly from the Lapgian, the Hamiltonian approach serving only as a justification. The wncepi of a Fock vacuum is generalized to several linear but coupled degrees of freedom.PACS number: 9880

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