Probing the Time Variation of a Fine Structure Constant Using Galaxy Clusters and the Quintessence Model

We explore a possible time variation of the fine structure constant (α ≅ e²/ℏc) using the Sunyaev-Zel'dovich effect measurements of galaxy clusters along with their X-ray observations. Specifically, the ratio of the integrated Comptonization parameter ${Y}_{\mathrm{SZ}}{D}_{A}^{2}$ and its X-ray counterpart Y_X is used as an observable to constrain the bounds on the variation of α. Considering the violation of the cosmic distance duality relation, this ratio depends on the fine structure constant of ~ α³. We use the quintessence model to provide the origin of α time variation. In order to give a robust test on α variation, two galaxy cluster samples, the 61 clusters provided by the Planck collaboration and the 58 clusters detected by the South Pole Telescope (SPT), are collected for analysis. Their X-ray observations are given by the XMM-Newton survey. Our results give $\zeta =-{0.203}_{-0.099}^{+0.101}$ for the Planck sample and $\zeta =-{0.043}_{-0.148}^{+0.165}$ for the SPT sample, indicating that α is constant with redshift within 3σ and 1σ for the two samples, respectively.