Quantum effects on higher dimensional space-time

Particle production in an odd-dimensional homogeneous universe with small anisotropy is discussed by using the effective action method. The pair production is a completely non-local phenomenon in an odd-dimensional theory, in contrast to the case of the familiar four-dimensional space-time. The effect of the closedness of the extra-dimensional space, i.e., the Casimir effect, which seems to be important in the scenario of Kaluza-Klein cosmology, is also discussed in the case of five dimensions.