Fine structure constant variation

In some extensions of the standard model of particle physics, the values of the fundamental coupling constants could vary in space and time, as they relate to the size of extra dimensions. Some recent observations of QSO have shown a possibility of time and spatial variation of the fine structure constant, alpha. We started our work by trying to understand the Bekenstein-Sandvik-Barrow-Magueijo (BSBM) model which places a cosmological scalar field and allows the field and alpha to evolve with the expansion of the universe and a low energy string theory model (Runaway Dilaton) that allows existence of a scalar field (known as Dilaton). Extensions of the scalar field in BSBM and the runaway of the dilaton allow us to consider strong and predict alpha variation across time and space. From those models, we then explore which models are allowed by QSO data by constraining free parameters and couplings: 10^-2< mass,m < 10²,  -.0002< coupling of BSBM, ζ/ω <.0006 (consistent within 2σ of QSO data in BSBM) and dilaton couplings (-.4< b_m<.4 , -1< Γ< 1) and then make predictions for variations in alpha at the surface of last scattering, which could be tested using the CMB.  After constraining the coupling parameters in both of these models we explored what happens at late times and we are currently using principal component analysis to find the likelihood functions of our parameter spaces.