Energy Conservation in Bekenstein's Theory for a Varying Fine-Structure Constant

Evidence from quasar absorption spectra indicates that the value of the fine-structure constant may have been slightly lower in the distant past. Jacob Bekenstein developed a cosmological scalar field theory that allows the value of the fine-structure constant to vary over space and time based on the density of charged matter. However, a typically used approximation to his theory does not conserve energy because energy is allowed to flow from matter into the scalar field, but not the other way around. The evolution equations in this theory were adjusted to conserve energy and the effect of this adjustment on the fine-structure constant variation compared to if energy was not conserved. Additionally, parameters in the energy conserved model were fit to Type Ia supernova data using Markov Chain Monte Carlo techniques.