Numerical Experiments in String Cosmology

TL;DR

The paper investigates classical string dynamics at high energy density using a tractable lattice model to test string-cosmology ideas, notably Brandenberger–Vafa’s mechanism for the emergence of 3 large spatial dimensions. It demonstrates a Hagedorn-like transition where short momentum modes saturate below $\rho_H$ and long winding strings carry the excess energy above $\rho_H$, with distinct distributions $dn/dE \propto E^{-(1+D/2)}$ for short strings and $dn/dE \propto 1/E$ for long strings. The lifetime of winding modes depends on spatial dimension: winding strings decay only for $D=3$ in the low-energy regime, while they persist for $D\ge4$, a result aligned with the proposed cosmological scenario. Overall, the study shows that a classical, exactly-evolved string lattice reproduces essential thermodynamic behavior of quantum strings and supports a dynamical explanation for the observed number of large spatial dimensions.

Abstract

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 dimensionality. 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 densionality. We find that in the low--energy density regime, long winding strings decay only if the space dimensionality 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 dimensionality and to avoid the initial singularity by means of string theory.