Is there further evidence for spatial variation of fundamental constants?

The detection of a spatial variation of the fine-structure constant, alpha, based on study of quasar absorption systems has recently been reported. The physics that causes this alpha-variation should have other observable manifestations, and this motivates us to look for complementary astrophysical effects. In this paper we propose a method to test whether spatial variation of fundamental constants existed during the epoch of big bang nucleosynthesis. Using existing measurements of primordial deuterium abundance we find very weak indications that such a signature might exist, but the paucity of measurements precludes any firm conclusion. We also examine existing quasar absorption spectra data that are sensitive to variation of the electron-to-proton mass ratio, mu, and x = (alpha^2 mu g_p) for spatial variation.