Time variation of fundamental constants, primordial nucleosynthesis, and the size of extra dimensions.

In theories with extra dimensions, the dependence of fundamental constants on the volume of the compact space allows one to use primordial nucleosynthesis to probe the structure of compact dimensions during the first few minutes after the big bang. Requiring the yield of primordial He to be within acceptable limits, we find that in ten-dimensional superstring models the size of the extra dimensions during primordial nucleosynthesis must have been within 0.5 jo of their current value, while in Kaluza-Klein models the extra dimensions must have been within 1% of their current