Dual spacetime and nonsingular string cosmology

Making use of the T-duality symmetry of superstring theory and of the double geometry from double field theory, we argue that cosmological singularities of a homogeneous and isotropic universe disappear. In fact, an apparent big bang singularity in Einstein gravity corresponds to a universe expanding to infinite size in the dual dimensions.

Figure 1

T versus $\log R$ for type II superstrings. Different curves are obtained for different entropy values, which are fixed. The larger the entropy is, the larger the plateau, given by the Hagedorn temperature. For $R=1$ we have the self-dual point.

Figure 2

The schematic solution for the scale factor in the string and Einstein frames for $D=4$. Note that the transition between the winding and momenta equation of state has been smoothed out, as is expected if (15) is considered.

Figure 3

The scale factor goes to zero only at $t_p\to -\infty$. Similarly its inverse goes to zero when $t_p\to \infty$.