Particle creation from vacuum by a nonstationary gravitational field in the canonical formalism

A study is made of particle creation from vacuum in isotropic and anisotropic models of the universe. By diagonalizing the Hamiltonian by Bogolyubov transformations, we obtain exact expressions for the particle number density and for the vacuum expectation values of the energy-momentum tensor of the created pairs. It is shown that near the singularity the equation of state of the created particles is $p\approx\varepsilon/3$. The problem of allowing for the reciprocal influence of particles on the metric is discussed.