The authors investigate finite-temperature quantum effects in multidimensional homogeneous cosmological models. They base their results on the full classification of such models. Their calculations concern the generalised Bianchi I model. However, they are of universal character. They investigate the back-reaction of the metric to quantum effects and show that they lead to dimensional reduction at low temperatures. The problem of the stability of the solutions is also discussed. They illustrate the influence of macrospace topology upon the effective action originating from gravitational and massless scalar fields.
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