Gauge-invariant perturbations of varying-alpha cosmologies

Using a gauge-invariant formalism we derive and solve the perturbed cosmological equations for the BSBM theory of varying fine structure 'constant'. We calculate the time evolution of inhomogeneous perturbations of the fine structure constant, on small and large scales with respect to the Hubble radius. In a radiation-dominated universe, small inhomogeneities in alpha will decrease on large scales but on scales smaller than the Hubble radius they will undergo stable oscillations. In a dust-dominated universe small inhomogeneous perturbations in alpha will become constant on large scales and on small scales they will increase as t(2/3), and deltaalpha/alpha will track deltarho(m)/rho(m). If the expansion accelerates, as in the case of a A or quintessence-dominated phase, inhomogeneities in alpha will decrease on both large and small scales. The amplitude of perturbations in alpha will be much smaller than that of matter or radiation perturbations. We also present a numerical study of the nonlinear evolution of spherical inhomogeneities in radiation and dust universes by means of a comparison between the evolution of flat and closed Friedmann models with time-varying alpha. Various limitations of these simple models are also discussed.