Hydrostatic mass of galaxy clusters within some theories of gravity

The mass of galaxy clusters (GCs) can be determined by calculating the hydrostatic equilibrium equation. In this work, we derive the hydrostatic mass of GCs within Eddington-inspired Born-Infeld (EiBI) theory, beyond Horndeski gravity (BHG), and modified emergent Newtonian gravity (MENG) with generalized uncertainty principle (GUP) correction. We apply the formulations on the masses of 10 GCs. We compare our results with the Newtonian mass of GCs. Within a regime, we get an insight that all formulations could match the Newtonian mass. Thus, the impact of the modified theories of gravity used in this work can be neglected in this regime. The noteworthy impact starts if we set $\kappa =5\times {10}^{40}$ m² for EiBI theory, $\Upsilon =-0.1655\times {10}^{69}$ for BHG, and ${\beta }_0=-1.656\times {10}^{110}$ for MENG. We also compare our results from EiBI theory and BHG with the baryonic masses $M_{bar}$ of the GCs. A better linear fit is achieved by EiBI theory with $\kappa =5.80\times {10}^{40}$ m², which gives the slope $M$ of $0.126\pm 0.086$. This value is closer to unity than the one of BHG. This leads us to the fact that EiBI theory is more effective than BHG in alleviating the mass discrepancy between hydrostatic mass and baryonic mass in GCs. Nevertheless, neither EiBI theory nor BHG completely addresses the mass discrepancy problem.