A principle to determine the number (3+1) of large spacetime dimensions

We assume that our universe originated from highly excited and interacting strings with coupling constant gs=O(1). Fluctuations of spacetime geometry are large in such strings and the physics dictating the emergence of a final spacetime configuration is not known. We propose that, nevertheless, it is determined by an entropic principle that the final spacetime configuration must have maximum entropy for a given amount of energy. This principle implies, under some assumptions, that the spacetime configuration that emerges finally is a (3+1)-dimensional FRW universe filled with w=1 perfect fluid and with 6-dimensional compact space of size ls; in particular, the number of large spacetime dimensions is d=3+1. Such an universe may evolve subsequently into our universe, perhaps as in Banks-Fischler scenario.