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We have investigated some cosmological consequences of variation of the finestructure constant, $\alpha$, in the context of theBekenstein-Sandvik-Barrow-Magueijo (BSBM) model. In this context, such avariation is attributed to electric charge by letting the latter take on thevalue of a real scalar field, $\phi$, which varies generally in space and time.We consider the dynamics of $\phi$ in the case that it is allowed to have anexponential potential. We have found solutions for evolutions of $\phi$ and$\alpha$ in the radiation and the matter dominated eras. By employingobservational bounds on the temporal variation of $\alpha$, we constrain themodel parameters. We then investigate the impact of $\alpha$-variation onredshift dependence of CMB temperature. It is shown that there is a deviationfrom the standard evolution of the temperature which contains two differentcontributions, one is important at high redshift eras and the other is mostlyeffective at low redshift eras.

Redshift Dependence of CMB Temperature in BSBM $\alpha$-Varying Theories