Superstring dominated early universe and epoch dependent gauge coupling

We have explored the possibility that the universe at very early stage was dominated by (macroscopic) heterotic strings. We have found that the dimensionless parameter $G\mu$ for the heterotic strings varies from $10^{-2}$ to $10^{-4}$ as the universe evolve from the matter dominance to radiation dominance. This led to the interesting consequence of epoch dependent gauge coupling constant. The gauge coupling constant at early times was found to be much stronger than the present strong interaction.