Numerical experiments on string cosmology

We investigate some classical aspects of fundamental strings via numerical experiments. In particular, we study the thermodynamics of a string network within a toroidal universe, as a function of string energy density and space dimension. We find that when the energy density of the system is low, the dominant part of the string is in the form of closed loops of the shortest allowed size, which correspond to the momentum string modes. At a certain critical energy density corresponding to the Hagedorn temperature, the system undergoes a phase transition characterized by the formation of very long loops, winding a number of times around the torus. These loops correspond to the winding string modes. As the energy density is increased, all the extra energy goes into these long strings. We then study the lifetime of winding modes as a function of the space dimension. We find that in the low-energy density regime, long winding strings decay only if the space dimension of the toroidal universe is equal to 3. This finding supports the proposed cosmological scenario by Brandenberger and Vafa, which attempts to explain the space dimension and to avoid the initial singularity by means of string theory.