Several attempts have been made in the past decades to search for the true ground state of the dense matter at sufficiently large densities and low temperatures via compact astrophysical objects. Focusing on strange stars, we derive the hydrostatic equilibrium assuming a maximally symmetric phase of homogeneous superconducting quark matter called the color-flavor-locked (CFL) phase in the background of energy–momentum squared gravity (EMSG). Theoretical and experimental investigations show that strange quark matter (SQM) in a CFL state can be the true ground state of hadronic matter at least for asymptotic densities, and even if the unequal quark masses. Motivated by these theoretical models, we explore the structure of stellar objects in recently proposed EMSG, which allows a correction term $T_{\mu \nu }{T}^{\mu \nu }$ in the action functional of the theory. Interestingly, EMSG may be effective to resolve the problems at high energy densities, e.g., relevant to the early universe and dense compact astrophysical objects without invoking some new forms of fluid stress, such as bulk viscosity or scalar fields. Finally, we solve the complicated field equations numerically to obtain the mass–radius relations for strange stars in CFL equation of state.

在过去的几十年中，人们进行了几次尝试，以通过紧凑的天体物体在足够大的密度和低温下寻找致密物质的真实基态。着眼于奇异的恒星，我们推导流体静力学平衡，假设在能量-动量平方重力（EMSG）的背景下，均相超导夸克物质的最大对称相称为色味锁定（CFL）相。理论和实验研究表明，至少在渐近密度下，即使夸克质量不相等，处于CFL状态的奇夸克物质（SQM）仍可能是强子物质的真实基态。基于这些理论模型，我们在最近提出的EMSG中探索了恒星物体的结构，该结构允许校正项${Ť}_{\mu \nu }{Ť}^{\mu \nu }$在理论的行动功能上。有趣的是，EMSG可以有效地解决高能量密度下的问题，例如与早期宇宙和致密致密的天体物体有关的问题，而无需调用某些新形式的流体应力，例如体积粘度或标量场。最后，我们用数值方法求解复杂的场方程，以获得CFL状态方程中奇异恒星的质量半径关系。