COSMOLOGICAL QUANTUM FLUCTUATIONS - GAUGE-INVARIANCE AND GAUSSIAN STATES

A quantum theory of cosmological perturbations is based on the action of Einstein gravity with matter expanded to quadratic order around a background solution of the field equations. If, in the Schrodinger picture, the wavefunction is assumed to factorize such that each factor is a function of only a finite number of degrees of freedom (e.g. Fourier components of the fields) all gauge constraints can be solved explicitly. This generalizes previous gauge-invariant quantizations while clarifying their limited scope. The result is cast into the more convenient Heisenberg picture. It can be found directly from the Lagrangian, the Hamiltonian approach serving only as a justification. The concept of a Fock vacuum is generalized to several linear but coupled degrees of freedom.