Modified dispersion relations from closed strings in toroidal cosmology

A long-standing problem of theoretical physics is the exceptionally small value of the cosmological constant $\Lambda \sim {10}^{-120}$ measured in natural Planckian units. Here we suggest how this tiny number might arise from a toroidal string cosmology based on closed strings. In this picture the dark energy would arise from a correlation between momentum and winding modes that for short distances has an exponential fall-off with increasing values of the momenta. The freeze-out by the expansion of the background universe for these trans-Planckian modes might be interpreted as a frozen condensate of the closed-string modes in the three noncompactified spatial dimensions. Our qualitative arguments are heuristic in nature and published only because they may suggest an improved treatment of the connection between strings and cosmological expansion.