A T-Duality-Protected Speed-of-Light Bounce in String Gas Cosmology

We study a varying-speed-of-light (VSL) phase embedded in string gas cosmology (SGC), with the effective propagation speed controlled by the dilaton during the Hagedorn era. For the exponential ansatz $c(\phi)=c_0\,e^{-\alpha\phi}$, the analytic Hagedorn background generates a speed-of-light bounce: an early superluminal phase ($c\gg c_0$), crossover at $t/t_0\approx 0.285$ for the branch studied here, and a collapse of $c$ toward zero as the self-dual regime is approached. The self-dual point at $R=\ell_s$ provides a T-duality anchor for matching onto the late-time branch with $c=1$. Evaluating the comoving horizon on this background, we find enhancement factors of $1.54$ and $3.44$ for $\alpha=1$ and $\alpha=2$, respectively, while the flatness parameter $\Omega-1\propto c^2/(a^2H^2)$ is found numerically to be suppressed by $10^{-4}$--$10^{-7}$ over the late Hagedorn phase. These results show that a dilaton-driven VSL phase can enlarge the causal horizon and suppress curvature within the controlled regime of SGC, while localizing the remaining obstruction to the self-dual matching point.