Abstract
Generic cosmological models in non-critical string theory have a time-dependent dilaton background at a late epoch. The cosmological deceleration parameter Q_0 is given by the square of the string coupling, g_s^2, up to a negative sign. Hence the expansion of the Universe must accelerate eventually, and the observed value of Q_0 coresponds to g_s^2 ~ 0.6. In this scenario, the string coupling is asymptotically free at large times, but its present rate of change is imperceptibly small.
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