| Summary: | We explore a possible time variation of the fine structure constant (α ≡ e²/â„c) 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_(SZ)D²_A 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 ζ = -0.203_(-0.099)^(+0.101) for the Planck sample and ζ = -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. © 2021. The American Astronomical Society. Received 2021 June 18; revised 2021 August 22; accepted 2021 August 24; published 2021 November 16. We thank the anonymous referee for the helpful and constructive feedback. This work was supported by the National Key R & D Program of China (2017YFA0402600), the Natural Science Foundation of Shandong Province, China (Grant NO.ZR2019MA059), and the National Natural Science Foundation of China (grant No. 11929301). Z.Z. is supported in part by NASA grant 15-WFIRST15-0008, Cosmology with the High Latitude Survey Roman Science Investigation Team (SIT). K.B. acknowledges Department of Science and Technology, Government of India for providing the financial support under the DST-INSPIRE Fellowship program. Published - Liu_2021_ApJ_922_19.pdf Accepted Version - 2109.00134.pdf
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