Constraining spatial variations of the fine-structure constant in symmetron models

We introduce a methodology to test models with spatial variations of the fine-structure constant $\alpha$, based on the calculation of the angular power spectrum of these measurements. This methodology enables comparisons of observations and theoretical models through their predictions on the statistics of the $\alpha$ variation. Here we apply it to the case of symmetron models. We find no indications of deviations from the standard behavior, with current data providing an upper limit to the strength of the symmetron coupling to gravity ($\log{\beta^2}<-0.9$) when this is the only free parameter, and not able to constrain the model when also the symmetry breaking scale factor $a_{SSB}$ is free to vary.