<![CDATA[The mass of galaxy cluster systems can be determined by calculating the hydrostatic equation for such systems. In this study, we derive the hydrostatic mass of galaxy cluster systems within the Eddington-inspired Born-Infeld (EiBI) theory, a modified theory of gravity. The EiBI theory is further modified by incorporating the generalized uncertainty principle (GUP) into its formulation. The GUP affects the mathematical expression of the temperature in galaxy clusters, leading to modifications in the clusters' equation of state (EoS), which is also an essential mathematical tool in hydrostatic equation calculations. This incorporation is motivated by the need to explore quantum gravitational effects on cosmological scales, bridging a fundamental gap between a modified theory of gravity and quantum mechanics. This work is significant in that it introduces the effect of the GUP, implemented through a modification of the temperature, within the framework of EiBI gravity. Using the derived formulation, we calculate the mass of 12 galaxy clusters and compare the results with observational data. The calculations reveal a significant reduction in the masses of these galaxy clusters to the order of 10-19 M⊙. A result which is profoundly inconsistent with observational data, thereby challenging the physical viability of this specific EiBI-GUP framework for modelling large-scale structures like galaxy clusters.]]>
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