Physical Viability of Dark Energy Compact Stars in f(R) Gravity Using Durgapal-Fuloria Solutions

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In this work, we investigate the physical viability and structural properties of compact stars within the framework of modified gravity, specifically f ( R ) gravity. Three distinct functional forms of the gravitational Lagrangian are considered, namely f ( R ) = R + α R 2 , f ( R ) = R + α R 2 ( 1 + γ R ) , and f ( R ) = R + α R ( e − R / γ − 1 ) , which allow us to explore both polynomial and exponential corrections to General Relativity. The interior spacetime is modeled using a static and spherically symmetric anisotropic fluid distribution, and the corresponding modified field equations are solved to obtain the energy density, radial pressure, and tangential pressure profiles. To assess the astrophysical relevance of the proposed models, we apply them to ten observed compact stellar candidates, namely Her X-1, SAX J1808.4-3658, SMC X-1, LMC X-4, Cen X-3, 4U 1820-30, PSR J1903+327, 4U 1608-52, Vela X-1, and PSR J1614-2230. The obtained solutions are examined through several physical acceptability criteria, including regularity conditions, energy conditions, causality, equilibrium via the generalized Tolman–Oppenheimer–Volkoff equation, and stability analyses. Furthermore, key observable quantities such as mass–radius relations, compactness, surface redshift, and anisotropy are discussed in detail for each model. Our results indicate that all three f ( R ) gravity models can support realistic and stable astrophysical compact star configurations, with noticeable deviations from General Relativity, particularly for higher curvature regimes, suggesting that modified gravity effects may play a significant role in describing ultra-dense stellar objects.