INTEGRABLE SCALAR FIELD MULTIDIMENSIONAL COSMOLOGIES

Multi-dimensional cosmological models with spacetime consisting of n ( n greater than or equal to 2) Einstein spaces M(i) are investigated in the presence of m (m greater than or equal to 1) non-interacting homo geneous minimally coupled scalar fields. An integrable class of models is found in the case of Ricci-flat factor-spaces Mi. These models are equivalent to an m-component perfect fluid with the equations of stat e P-(a) = (alpha((a)) - 1)rho((a)) (a = 1,...,m; alpha((a)) = constant ). An explicit form of the scalar field potentials is found for specia l cases. Classical as well as quantum behaviour of the universe is inv estigated. Some of the solutions produce inflation from 'nothing'. Cla ssical Euclidean wormhole solutions are also found.