Quantized scalar field in Friedmann–Lobachevskii space

A quantized scalar field is considered in an open Friedmann universe wich a Lorentz invariant spatial part. Since the Friedmann universe is nomstationary, the energy of a free field is a not conserved and the Hamiltonian is not diagonal in the creation and annihilation operators. The Hamiltonian is diagonaliized by means of a set of $\eta$-dependent representations ($\eta$ is the time) of the commutation relations with Lorentz invariant vacuum states. The $\eta$-wacuum mean value of the operator of the number density of particles corresponding to the $\eta_0$ representation ($\eta>\eta_0$) is caleulated. The question of $\eta$ a quasielassieal limit is discussed and a transition is made to flat space-time.