Mass–radius behavior of dark energy–influenced compact stars in modified Gauss–Bonnet gravity

This research presents a relativistic model for anisotropic compact stars made up of baryonic matter influenced by a dark energy (DE) component. The model is developed within the framework of modified gravity, specifically the [Formula: see text] theory, where [Formula: see text] denotes the Gauss–Bonnet term and [Formula: see text] is the trace of the energy–momentum tensor. To account for the impact of DE, an equation of state (EoS) with a coupling parameter [Formula: see text] is employed. This parameter governs the interaction between matter content and spacetime geometry. The internal geometry of the stellar object is described using the Finch–Skea metric, which is particularly suited for modeling systems with pressure anisotropy in the presence of DE. The physical viability of the model is tested using observational data from the pulsar PSR J0348+0432, which has a measured mass of [Formula: see text] and a radius of approximately 12.072 km. This allows for a detailed analysis of how variations in the coupling constant [Formula: see text] influence fundamental properties such as energy density, pressure anisotropy, and the resulting mass–radius (M–R) relationship. Our analysis shows that lower values of [Formula: see text] lead to a stiffer EoS due to stronger coupling between matter and curvature. Interestingly, the M–R relation remains stable across variations in [Formula: see text], ensuring consistency with astrophysical bounds. This modeling approach is versatile and extendable to other compact stellar systems, offering insight into the role of modified gravity in stellar dynamics.