Parameter Constraints on $f(R^{1+ε},T_{μν}T^{μν})$ Gravity from Exotic Compact Objects
According to General Relativity (GR), gravity is described as the curvature of spacetime caused by mass and energy. Although GR has been highly successful in describing gravitational phenomena, exotic compact objects with high mass and strong gravitational fields, as well as low-mass objects, have motivated the study of modified theories of gravity. One of the modified gravity frameworks is $f(R,T^2) = R^{1 + ε} + ακ^2 T_{μν} T^{μν}$, which provides an extension of GR by introducing modifications to both the geometric and matter sectors. In this study, we investigate the mass-radius structure, physical viability, and stability of quark stars in $f(R,T^2)$ gravity using the MIT Bag Model equation of state. We compare results from the exact $f(R,T^2)$ model, its first-order Taylor expansion, and GR. The values of the gravity parameter $ε$ and $α$ are constrained by evaluating the ability of the model to reproduce the observed mass-radius configurations of compact objects, including HESS J1731-347 with a mass of $M = 0.77_{-0.17}^{+0.20} \, M_{\odot}$ and a radius of $R = 10.4_{-0.78}^{+0.86}$ km, GW190814 with a mass of $M = 2.6 \, M_{\odot}$, PSR J1614-2230, with a mass of $M = 1.928 \pm 0.017 \, M_{\odot}$ and a radius of $R > 10$ km, and PSR J0437-4715, with a mass of $M = 1.418 \pm 0.037 \, M_{\odot}$ and a radius of $R = 11.36_{-0.63}^{+0.95}$ km. We assess the physical viability and stability of the stellar configurations using the energy conditions (strong, weak, null, and dominant) and the speed of sound. Overall, the $f(R,T^2)$ gravity model can accommodate quark star configurations and reproduce the observed properties of massive compact objects, particularly those associated with GW190814 and the lightest compact object observed, HESS J1731-347, respectively.