String cosmology backgrounds from classical string geometry

We introduce a very early universe model based on the thermodynamics of a gas of closed strings in a background that is nonperturbative in ${\alpha }^{\prime }$. Upon considering the fully ${\alpha }^{\prime }$-corrected equations extended to include certain anisotropic cosmological backgrounds, we describe the evolution of the system in three different stages parametrized by the gas’s equation of state. Using standard string thermodynamical arguments, we start with an isotropic ten-dimensional universe inside the string scale and evolve it toward a universe with four large spacetime dimensions and six stabilized internal dimensions in the Einstein frame.

Figure 1

The dynamics of the model is shown as a whole, which is later separated into three different stages in Sec. 4. On the left, the evolution of the equation of state is plotted as a function of time for both the internal and the external directions. In the center, the time evolution of the scale factor and the Hubble radius can be seen in the string frame while on the right they are shown in the Einstein frame. The dilaton stabilizes at $t_{*}$. The evolution is nonsingular in both frames.