Particle creation effect on M₄×S⁷ Kaluza-Klein cosmologies

The particle creation effect on the higher-dimensional Kaluza-Klein cosmologies with M₄×S⁷ topology is studied. This quantum effect is found to change the classical behavior of the internal and external scale factors drastically in the early stage of the expansion, so that the dimensional reduction seems to fail. However, at the later stage two scale factors get separated from each other and the internal scale factor approaches the final singularity just like the vacuum case.