Testing possible variations in fundamental constants of nature is a crucial endeavor in observational cosmology. This paper investigates potential cosmological variations in the fine structure constant (α) through a non-parametric approach, using galaxy cluster observations as the primary cosmological probe. We employ two methodologies based on galaxy cluster gas mass fraction measurements derived from X-ray and Sunyaev–Zeldovich observations, along with luminosity distances from type Ia supernovae. We also explore how different values of the Hubble constant (H0) impact the variation of α across cosmic history. When using the Planck satellite’s H0 observations, a constant α is ruled out at approximately the 3σ confidence level for z≲0.5. Conversely, employing local estimates of H0 restores agreement with a constant α.
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