In this paper, we investigate a possible time variation of the gravitational constant ($G$) using a nonparametric approach. Our main cosmological probe is the gas mass fraction of galaxy clusters measured from x-ray observations. We also account for the effect of a varying $G$ on the intrinsic luminosity of type Ia supernovae (SNe Ia) through the Chandrasekhar mass–luminosity relation. We consider a specific phenomenological scenario, motivated by some scalar-tensor and screened modified-gravity frameworks, in which the standardized luminosity of SNe Ia decreases with increasing Chandrasekhar mass. Using gas mass fraction measurements jointly with luminosity distances from the Pantheon+ compilation, we reconstruct the evolution of $G$ through Gaussian processes. Our results indicate that a constant gravitational coupling remains broadly consistent with the data, although mild low-redshift departures are allowed.

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• Alternative gravity theories
• Cosmological parameters
• General relativity