SEMICLASSICALITY AND DECOHERENCE OF COSMOLOGICAL PERTURBATIONS

Transition to the semiclassical behaviour and the decoherence process for inhomogeneous perturbations generated from the vacuum state during an inflationary stage in the early Universe are considered in both th e Heisenberg and the Schrodinger representations to show explicitly th at both approaches lead to the same prediction: the equivalence of the se quantum perturbations to classical perturbations having stochastic Gaussian amplitudes and belonging to the quasi-isotropic mode. This eq uivalence and the decoherence are achieved once the exponentially smal l (in terms of the squeezing parameter r(k)) decaying mode is neglecte d. In the quasi-classical limit \r(k)\ --> infinity, the perturbation mode functions can be made real by a time-independent phase rotation; this is shown to be equivalent to a fixed relation between squeezing a ngle and phase for all modes in the squeezed-state formalism. Though t he present state of the gravitational wave background is not a squeeze d quantum state in the strict sense and the squeezing parameters loose their direct meaning due to interaction with the environment and othe r processes, the standard predictions for the rms values of the pertur bations generated during inflation are not affected by these mechanism s (at least, for scales of interest in cosmological applications). Thi s stochastic background still occupies a small part of phase space.