Dark energy generated from a (super-) string effective action with higher-order curvature corrections and a dynamical dilaton

We investigate the possibility of a dark energy universe emerging from an action with higher-order string loop corrections to Einstein gravity in the presence of a massless dilaton. These curvature corrections (up to R4 order) are different depending upon the type of (super-) string model which is considered. We find in fact that type II, heterotic, and bosonic strings respond differently to dark energy. A dark energy solution is shown to exist in the case of the bosonic string, while the other two theories do not lead to realistic dark energy universes. A detailed analysis of the dynamical stability of the de Sitter solution is presented for the case of a bosonic string. A general prescription for the construction of a de Sitter solution for the low-energy (super-) string effective action is also indicated. Beyond the low-energy (super-) string effective action, when the higher-curvature correction coefficients depend on the dilaton, the reconstruction of the theory from the expansion history of the universe is done with a corresponding prescription for the scalar potentials