Non-parametric reconstruction of the fine structure constant with galaxy clusters

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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 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 H 0 ) impact the variation of α α across cosmic history. When using the Planck satellite’s H₀ H 0 observations, a constant α α is ruled out at approximately the 3 σ σ confidence level for z 0.5 z ≲ 0.5 . Conversely, employing local estimates of H₀ H 0 restores agreement with a constant α α .