Integrable higher-dimensional cosmology with separable variables in an Einstein-dilaton-antisymmetric field theory

We consider a $D$-dimensional cosmological model with a dilaton field and two $(D-d-1)$-form field strengths which have nonvanishing fluxes in extra dimensions. Exact solutions for the model with a certain set of couplings are obtained by separation of three variables. Some of the solutions describe accelerating expansion of the $d$-dimensional space. Quantum cosmological aspects of the model are also briefly mentioned.