The lowest-order string-gravity equations introduced in the previous chapters will be applied in this chapter to the case of homogeneous cosmological backgrounds, and will be shown to be invariant under an important class of transformations associated with the so-called “duality” symmetries of the string effective action. These symmetries cannot be implemented in the context of the standard general-relativity equations, as they require the presence of the full massless multiplet of states of the closed bosonic string spectrum (the metric, the dilaton and the antisymmetric tensor field), coupled exactly as predicted by the string effective action (see Chapter 3). It will be shown that, by exploiting these symmetries, it is possible to obtain new cosmological solutions starting from known configurations, typical of the standard scenario. These new solutions may suggest possible scenarios for the primordial evolution of our Universe.

It should be recalled that the above-mentioned cosmological symmetries represent the extension to time-dependent backgrounds of the so-called “target space duality” (or T-duality) symmetry, present in the spectrum of a closed bosonic string propagating in a manifold in which some spatial dimensions are compact [1, 2]. It is well known, in fact, that the spatial periodicity along such directions (topologically equivalent to a circle or, more generally, to a higher-dimensional torus), implies the quantization of the conjugate momenta, p → pn = n/R, where n is an integer and R is the (constant) radius of the compact dimensions.