  We study the space-time evolution of the fine structure constant, $\alpha$,
inside evolving spherical overdensities in a lambda-CDM Friedmann universe
using the spherical infall model. We show that its value inside virialised
regions will be significantly larger than in the low-density background
universe. The consideration of the inhomogeneous evolution of the universe is
therefore essential for a correct comparison of extragalactic and solar system
limits on, and observations of, possible time variation in $\alpha$ and other
constants. Time variation in $\alpha$ in the cosmological background can give
rise to no locally observable variations inside virialised overdensities like
the one in which we live, explaining the discrepancy between astrophysical and
geochemical observations.
