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Dilaton Brane Cosmology with Second Order String Corrections and the Cosmological Constant

We consider, in five dimensions, the effective action from heterotic string which includes quantum gravity corrections up to (a')^2. The expansion, in the string frame, is in terms of |a'R|, where R is the scalar curvature and uses the third order Euler density, next to the Gauss-Bonnet term. For a positive tension brane and infinite extra dimension, the logarithmic class of solutions is less dependent from fine-tuning problems than in previous formulations. More importantly, the model suggests that in the full non-perturbative formulation, the string scale can be much lower than the effective Planck mass, without the string coupling to be vanishingly small. Also a less severe fine-tuning of the brane tension in needed.