Evolution of the Fine Structure Constant Driven by Dark Matter and the Cosmological Constant

Bekenstein's model of a scalar field, \phi, that affects the electromagnetic permeability (usually identified with ``changing \alpha'') predicts tiny variations of the effective fine structure constant up to very high red-shifts, |\alpha(z=3.5)/\alpha_0-1| < 10^{-10}, when the constraints from E\"otv\"os-Dicke-Braginsky types of experiments are imposed. We generalize this model by allowing additional couplings of \phi to both a dark matter candidate and to the cosmological constant. We show that in a supersymmetric generalization of Bekenstein's model, the coupling to the LSP, which is assumed to contribute significantly to the dark matter density, can be up to six orders of magnitude stronger than the coupling to the baryon energy density. This allows one to evade the present limits on the non-universality of the gravitational attraction due to \phi-exchange and at the same time accommodate the effective shift in \alpha at the level of \alpha(z=3.5)/\alpha_0-1 \sim 10^{-5}, reported recently from observations of quasar absorption spectra.