  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.
