A cosmic microwave background search for fine-structure constant evolution

In some extensions of the standard model of particle physics, the values of the fundamental coupling constants vary in space and time. Some observations of quasars hint at time and spatial variation of the fine structure constant $\alpha$. Here, the Bekenstein-Sandvik-Barrow-Magueijo (BSBM) model (which posits the existence of a scalar field driving evolution in the fundamental electric charge $e$) is tested against quasar and Planck satellite cosmic microwave background (CMB) data. In this model, variations in $e$ are coupled to the matter density through a factor $\zeta_{\rm m}/{\omega}$, which is related to electromagnetic contributions to nucleon masses, and {the energy} scale of new physics. Simulations conducted here do not support claims that the electrostatic contribution to $\zeta_{m}$ is completely shielded. Other common approximations used in BSBM field evolution are found to be adequate. Principal components of the CMB data with respect to variations in $\alpha$ are used to obtain constraints of $\zeta_{\rm m}/{\omega}\lesssim 9.3 \times 10^{-9}$ for a massless field. A forecast anticipating the promise of the Simons Observatory (SO) CMB experiment shows that SO will be sensitive to values of $\zeta_{\rm m}/{\omega}\geq 2.2 \times 10^{-9}$.