  A possibility to describe quantum gravitational fluctuations of the spacetime
background is provided by virtual $D$-branes. These effects may induce a tiny
violation of the Lorentz invariance (as well as a possible violation of the
equivalence principle). In this framework, we study the formation of light
elements in the early Universe (Big Bang Nucleosynthesis). By using the Big
Bang Nucleosynthesis observations, We infer an upper bound on the topological
fluctuations in the spacetime foam vacuum $\sigma^2$, given by $\sigma^2
\lesssim 10^{-22}$.
