Dark matter admixed quark stars in Gravity's rainbow framework: A feasibility study based on observational data

In this work, we study structural and stability properties of dark matter-admixed quark stars (DMQS) utilizing a two-fluid formalism, incorporating the effects of Rainbow Gravity (RG) that introduces energy-dependent modifications to spacetime geometry. We solve the modified Tolman-Oppenheimer-Volkoff (TOV) equations with energy-dependent spacetime metrics by considering the MIT Bag model for quark matter and a self-interacting bosonic dark matter. We investigate the effect of the interaction between dark matter fractions and RG parameters on the mass-radius relation, tidal deformability and stability criteria of these compact objects. Our results show that RG induces significant changes in the stellar structure and allows for more massive and compact objects than the general relativity counterpart. Notably, recent high-precision astrophysical data, including those from NICER measurement of PSR J0740+6620 and gravitational wave measurements (e.g., GW170817) greatly support our derived mass-radius relations and tidal deformability bounds in the observational limits. We find that DMQS in RG serve as a new class of compact objects, which gives us a better understanding of how exotic matter and modified gravity can affect observable astrophysical phenomena.