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.