Quantum effects in multidimensional homogeneous cosmological models

Finite-temperature quantum effects in multidimensional homogeneous cosmological models are investigated, and results are based on the full classification of such models. These calculations concern the generalized Bianchi I model. However, they are of universal character. The back-reaction of metric to quantum effects leads to dimensional reduction at low temperatures. The problem of the stability of the solutions is also discussed. The influence of macrospace topology upon the effective action originating from gravitational and massless scalar fields is illustrated.