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 $$\alpha $$ α and the degree of anisotropy $$\beta $$ β . 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 $$\gamma _r$$ γ r , and the radial and transverse sound speeds $$v_r^2$$ v r 2 and $$v_t^2$$ v t 2 . Our results show that positive $$\alpha $$ α and positive anisotropy $$(\beta > 0)$$ ( β > 0 ) systematically increase the maximum mass and radius, enabling then configurations that exceed $$2\,M_\odot $$ 2 M ⊙ 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 $$(\alpha ,\beta )$$ ( α , β ) 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.