Ricci–Gauss–Bonnet Holographic Dark Energy: Thermodynamic Analysis and Extension to f ( G ) Gravity

This work presents a unified treatment of Ricci–Gauss.Bonnet holographic dark energy (RGB–HDE) (Physical Review D, 97(6), 064035), a particular case of the most generalized Nojiri-Odintsov HDE (Eur. Phys. J. C 77, 528), encompassing its cosmological dynamics, thermodynamic behavior, and its realization within f(G) gravity. Using a spatially flat FRW background, we analysed the equation of state(EoS) parameter for three different interaction scenarios. The results revealed transitions between quintessence and phantom regimes. Stability was analysed through squared speed of sound. From thermodynamic perspective, the generalised second law of thermodynamics(GSLT) was verified. The reconstructed f(G) model exhibited f(G(t)) → 0 as t → 0, ensuring recovery to general relativity at early times, while its late time behaviour drives accelerated expansion. The study demonstrates that the RGB-HDE framework provides a self consistent cosmological scenario unifying thermodynamic consistency with late time acceleration.