A Generalized Theory of Varying Alpha

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In this paper, we formulate a generalization of the simple Bekenstein-Sandvik-Barrow-Magueijo (BSBM) theory of varying alpha by allowing the coupling constant, \omega, for the corresponding scalar field \psi\ to depend on \psi.

• We focus on the situation where \omega\ is exponential in \psi\ and find the late-time behaviours 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 BSBM theory, and establish a cosmic no-hair behaviour for accelerating universes.