DYNAMICAL TOPOLOGY CHANGE, COMPACTIFICATION AND WAVES IN STRING COSMOLOGY

Exact string solutions are presented, where moduli fields are varying with time. They provide examples where a dynamical change of the topol ogy of space is occurring. Some other solutions give cosmological exam ples where some dimensions are compactified dynamically or simulate pr e-big bang type scenarios. Some lessons are drawn concerning the regio n of validity of effective theories and how they can be glued together , using stringy information in the region where the geometry and topol ogy are not well defined from the low energy point of view. Other time dependent solutions are presented where a hierarchy of scales is abse nt. Such solutions have dynamics which is qualitatively different and resemble plane gravitational waves.