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A long-standing problem of theoretical physics is the exceptionally smallvalue of the cosmological constant $\Lambda \sim 10^{-120}$ measured in naturalPlanckian units. Here we derive this tiny number from a toroidal stringcosmology based on closed strings. In this picture the dark energy arises fromthe correlation between momentum and winding modes that for short distances hasan exponential fall-off with increasing values of the momenta.The freeze-out bythe expansion of the background universe for these transplanckian modes may beinterpreted as a frozen condensate of the closed-string modes in the threenon-compactified spatial dimensions.Comment: 21 pages LaTeX. Clarification at end of Section 3. Modified  Discussion Section. Two notes added. Title change

Modified dispersion relations from closed strings in toroidal cosmology