A Generalized Theory of Varying Alpha
  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. 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.
