Alpha' - exact Backgrounds for String Cosmology

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I will discuss a novel approach to time-dependent background fields of string theory, which allows the identification of configurations which satisfy the conformal invariance conditions to all orders in the Regge slope parameter alpha'. I will present a graviton, dilaton and tachyon configuration which is a resummation of all orders in the Regge slope and is shown to satisfy the conformal invariance conditions order by order, to all orders in alpha', up to field redefinitions which do not change the dependence of the fields on the target space-time coordinates, due to a property termed as "homogeneity" of the Weyl anomaly coefficients. It describes an inflationary universe in the sigma-model frame, while in the Einstein frame it corresponds either to a de Sitter or to a power-law universe, depending on the values of the dilaton and the tachyon amplitudes. Possible ways to connect these different solutions, which may correspond to different epochs of the universe, will also be discussed.