Possible existence and physical features of mathematical models of dark energy ultra-compact objects in modified symmetric teleparallel gravity

Recent advances in modeling compact astrophysical objects have focused on incorporating dark energy as a relativistic component within their internal structures, offering novel insights into extreme matter configurations. Theoretical frameworks now explore anisotropic pressure profiles and modified equations of state, enabling predictions about stability and mass-radius relationships under dark energys repulsive influence. Such studies aim to resolve discrepancies in observed compact object populations while probing interactions between high-density matter and cosmological vacuum energy. This study presents a new analytical framework for a two-fluid system consisting of ordinary baryonic matter and dark energy in modified f(Q) gravity, with f(Q)=ξ+χQ, where ξ and χ are coupling constants. By utilizing the Durgapal-Lake metric potentials (Durgapal et al., Gen. Relativ. Gravit. 17:671, 1985, Lake K, Phys. Rev.D 67:10 2003) as seed solutions and assuming a linear equation of state for dark energy, the modified gravitational field equations are solved to derive exact interior solutions. The model parameters, including the dark energy coupling constant and constants from the metric ansatz, were determined by smoothly matching the interior geometry with the exterior spacetime at the stellar boundary. Observational data from three compact stars (HerX−1, 4U1538−52, SAXJ1808.4−3658) were used to test the model’s viability and regularity. The study included a thorough physical analysis, examining energy density gradients, anisotropy, stability, equilibrium conditions using the modified TOV equation. The results align with observational data, indicating that the model offers a physically plausible description of compact stars while maintaining stability and equilibrium under the tested conditions.