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 $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> and the degree of anisotropy $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> . 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 $$\gamma _r$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>r</mml:mi> </mml:msub> </mml:math> , and the radial and transverse sound speeds $$v_r^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>v</mml:mi> <mml:mi>r</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> and $$v_t^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>v</mml:mi> <mml:mi>t</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> . Our results show that positive $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> and positive anisotropy $$(\beta &gt; 0)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>β</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> systematically increase the maximum mass and radius, enabling then configurations that exceed $$2\,M_\odot $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mspace/> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:mrow> </mml:math> 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 $$(\alpha ,\beta )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>β</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> 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.