Generalized theory of varying alpha

In this paper, we formulate a generalization of the simple Bekenstein-Sandvik-Barrow-Magueijo theory of varying alpha by allowing the coupling constant ω for the corresponding scalar field ψ to depend on ψ. We focus on the situation where ω is exponential in ψ and find the late-time behaviors that occur in matter-dominated and dark-energy dominated cosmologies. We also consider the situation when the background expansion scale factor of the Universe evolves in proportion to an arbitrary power of the cosmic time. We find the conditions under which the fine-structure ``constant'' increases with time, as in the Bekenstein-Sandvik-Barrow-Magueijo theory, and establish a cosmic no-hair behavior for accelerating universes. We also find the conditions under which the fine-structure constant can decrease with time and compare the whole family of models with astronomical data from quasar absorption spectra.