VARIATIONS OF KALUZA-KLEIN COSMOLOGY

We investigate the cosmological consequences of having quantum fields living in a space with compactified dimensions. We will show that the equation of state is not modified by topological effects and so the dy namics of the universe remains as it is in the infinite volume limit. On the contrary the thermal history of the universe depends on terms t hat are associated with non-trivial topology. In the conclusions we di scuss some issues about the relationship between the c = 1 non-critica l string-inspired cosmology and the result obtained with matter given by a hot massless field in S1 x R.