Reconstruction of f(G) Gravity with Tsallis Holographic Dark Energy Using Granda–Oliveros Cutoff and Hybrid Scale Factor

This work presents a reconstruction framework of modified gravity in the presence of Tsallis holographic dark energy (THDE) by employing the Granda–Oliveros infrared cutoff together with a hybrid scale factor describing cosmic evolution. The hybrid scale factor successfully characterizes the transition from an early decelerated phase to the present accelerated expansion of the Universe, making the model suitable for studying realistic cosmological dynamics. Using the modified Friedmann equations in gravity, the corresponding reconstructed form of the gravitational function is obtained and analyzed in detail. The evolutionary behavior of the reconstructed equation of state (EoS) parameter is investigated to understand the nature of dark energy and the accelerated expansion scenario. The analysis shows that the EoS parameter exhibits quintessence and phantom-like behavior depending on the model parameters, indicating a rich cosmological structure.

Further, the physical viability of the reconstructed model is examined through stability analysis using the squared sound speed and the adiabatic index. In addition, the thermodynamic consistency of the reconstructed THDE model is tested through the generalized second law (GSL) of thermodynamics. The validity of the GSL throughout cosmic evolution confirms the thermodynamic feasibility of the model. Overall, the reconstructed gravity model with Tsallis holographic dark energy and Granda–Oliveros cutoff within the hybrid scale factor framework provides a consistent and stable description of the late-time accelerating Universe compatible with thermodynamic principles.