Dark-Energy Anisotropic Compact Configurations in 4D Einstein-Gauss-Bonnet Gravity: From Structure to Observational Viability

Abstract

We address the equilibrium configurations and stability properties of anisotropic compact stars whose interior is described by a modified Chaplygin gas (MCG) equation of state in the framework of the regularized four-dimensional Einstein-Gauss-Bonnet (4DEGB) theory. Applying a quasi-local prescription for the pressure anisotropy, we derive the modified Tolman-Oppenheimer-Volkoff (TOV) equations and integrate them numerically over a large parameter space in the Gauss-Bonnet coupling $\alpha$ and the degree of anisotropy $\beta$. We provide mass-radius sequences, mass-compactness, energy density, and pressure profiles, and perform a full stability analysis based on the turning-point criterion, the radial adiabatic index $\gamma_r$, and the radial and transverse sound speeds $v_r^2$ and $v_t^2$. Our results show that positive $\alpha$ and positive anisotropy $(\beta > 0)$ systematically increase the maximum mass and radius, enabling then configurations that exceed $2\,M_\odot$ while still obeying causality and the modified Buchdahl bound in 4DEGB gravity. A comparison with the latest astrophysical constraints (NICER, GW170817, GW190814, and massive-pulsar measurements) identifies regions of the $(\alpha,\beta)$ parameter space that are observationally allowable. In conclusion, anisotropic dark-energy stars in 4DEGB gravity provide viable, observationally testable ultra-compact alternatives to normal neutron stars and black holes, and also potentially open rich avenues for further multi-messenger searches for higher-curvature effects.