  In this work we investigate the utility of using SNe Ia observations in
constraining the cosmological parameters in BSBM theory where a scalar field is
responsible for both fine structure constant variation and late time universe
acceleration. The model is discussed in the presence of an exponential self
potential for the scalar field. Stability and phase space analysis of the
solutions are studied. The model is tested against observational data for
Hubble parameter and quasar absorption spectra. With the best fitted model
parameters, the theory predicts a good match with the experimental results and
exhibits fine structure constant variation. The analysis also shows that for
the equation of state parameter, recent universe acceleration and possible
phantom crossing in future is forecasted.
