  Transition from quantum to semiclassical behaviour and loss of quantum
coherence for inhomogeneous perturbations generated from a non-vacuum initial
state in the early Universe is considered in the Heisenberg and the
Schr\"odinger representations, as well as using the Wigner function. We show
explicitly that these three approaches lead to the same prediction in the limit
of large squeezing (i.e. when the squeezing parameter $|r_k|\to \infty$): each
two-modes quantum state (k, -k) of these perturbations is equivalent to a
classical perturbation that has a stochastic amplitude, obeying a non-gaussian
statistics which depends on the initial state, and that belongs to the
quasi-isotropic mode (i.e. it possesses a fixed phase). The Wigner function is
not everywhere positive for any finite $r_k$, hence its interpretation as a
classical distribution function in phase space is impossible without some
coarse graining procedure. However, this does not affect the transition to
semiclassical behaviour since the Wigner function becomes concentrated near a
classical trajectory in phase space when $|r_k|\to \infty$ even without coarse
graining. Deviations of the statistics of the perturbations in real space from
a Gaussian one lie below the cosmic variance level for the N-particles initial
states with N=N(|k|) but may be observable for other initial states without
statistical isotropy or with correlations between different k modes. As a way
to look for this effect, it is proposed to measure the kurtosis of the angular
fluctuations of the cosmic microwave background temperature.
