Dilation, winding modes and cosmological solutions

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Abstract
The author reviews some formal aspects of cosmological solutions in closed string theory with duality symmetric 'matter' emphasizing the necessity to account for the dilaton dynamics for a proper incorporation of duality. The author considers two models: when the matter action is the classical action of the fields corresponding to momentum and winding modes and when the matter action is represented by the quantum vacuum energy of the string compactified on a torus. Assuming that the effective vacuum energy is positive one finds that in both cases the scale factor undergoes oscillations from maximal to minimal values with the amplitude of oscillations decreasing to zero or increasing to infinity depending on whether the effective coupling (dilaton field) decreases or increases with time. The contribution of the winding modes to the classical action prevents infinite expansion. Duality is spontaneously broken on a solution with generic initial conditions.
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