Reconstruction of f(G) Gravity from an Interacting Viscous Generalized QCD Ghost Dark Energy Model: Cosmology and Thermodynamics: Cosmology and Thermodynamics
In this work, we investigate an interacting viscous generalized QCD ghost dark energy model in the framework of reconstructed $f(G)$ gravity proposed in Phys.\ Lett.\ B 631, 1--6 (2005). The interaction between dark matter and dark energy together with bulk viscosity is incorporated to describe a more realistic cosmic evolution. A hybrid expansion law is adopted to reconstruct the modified Gauss-Bonnet function, which naturally connects the early matter-dominated epoch with the present accelerated expansion of the universe. Since an exact analytical reconstruction is difficult, the $f(G)$ function is obtained numerically in both the early- and late-time regimes. Motivated by the numerical reconstruction, a reconstruction-inspired power-law form of $f(G)$ is also considered to examine the cosmological implications of the model. The results show that the reconstructed $f(G)$ function evolves smoothly throughout the cosmic history, while the effective equation of state gradually approaches the de Sitter phase at late times. The thermodynamic behavior of the model is further examined using Barrow entropy following Eur.\ Phys.\ J.\ C 81, 644 (2021). The non-negative evolution of the total entropy shows the validity of the generalized second law of thermodynamics. The study finally concludes that the interacting viscous generalized QCD ghost dark energy model in reconstructed $f(G)$ gravity provides a viable and thermodynamically consistent framework for explaining the late-time accelerated expansion of the universe.