Stabilisation of Seven Directions in an Early Universe M -- theory Model

Our model consists of intersecting 22'55' branes in M theory distributed uniformly in the common transverse space. Equations of state follow from U duality symmetries. In this model, three spatial directions expand, and seven directions stabilise to constant sizes. From string theory perspective, the dilaton is hence stabilised. The constant sizes depend on certain imbalance among initial values. One naturally obtains M_{11} \simeq M_s \simeq M_4 and g_s \simeq 1 within a few orders of magnitude. Smaller numbers, for example M_s \simeq 10^{- 16} M_4, are also possible but require fine tuning.