Behavior of varying-alpha cosmologies

Abstract

We determine the behavior of a time-varying fine structure ``constant'' $\ensuremath{\alpha}(t)$ during the early and late phases of universes dominated by the kinetic energy of changing $\ensuremath{\alpha}(t),$ radiation, dust, curvature, and lambda, respectively. We show that after leaving an initial vacuum-dominated phase during which $\ensuremath{\alpha}$ increases, $\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}$ tends rapidly to a constant value. The effect of an early period of de Sitter or power-law inflation is to drive $\ensuremath{\alpha}$ to a constant value. Various cosmological consequences of these results are discussed with reference to recent observational studies of the value of $\ensuremath{\alpha}$ from quasar absorption spectra and to the existence of life in expanding universes.