Cosmological models with a quantum scalar field

Self-consistent solutions for the evolution of isotropic cosmological models filled with quantum massive scalar field with conformal relation with gravitation are investigated. As initial state vacuum field state is accepted, vacuum being determined as field state with the least energy. Two possible types of Einstein equation modifications for account of a local independent on mass contribution into conformal anomaly vacuum polarization are investigated. It is shown that gravitational field equations with higher derivatives lead to singularities. Minimal modification of Einstein equations admits non singular cosmological models, however the production processes of vacuum quasiparticles are of many orders less than those required for the model operation under realistic Friedman regime