Behavior of varying-alpha cosmologies

We determine the behavior of a time-varying fine structure “constant” $\alpha \mathrm{}\left(t\right)\mathrm{}$ during the early and late phases of universes dominated by the kinetic energy of changing $\alpha \mathrm{}\left(t\right),$ radiation, dust, curvature, and lambda, respectively. We show that after leaving an initial vacuum-dominated phase during which $\alpha$ increases, $\alpha$ remains constant in universes such as our own during the radiation era, and then increases slowly, proportional to a logarithm of cosmic time, during the dust era. If the universe becomes dominated by a negative curvature or a positive cosmological constant then $\alpha$ tends rapidly to a constant value. The effect of an early period of de Sitter or power-law inflation is to drive $\alpha$ to a constant value. Various cosmological consequences of these results are discussed with reference to recent observational studies of the value of $\alpha$ from quasar absorption spectra and to the existence of life in expanding universes.