Ricci–gauss–bonnet holographic dark energy: Thermodynamic analysis and extension to f(G) gravity

This paper presents a unified treatment of [E. N. Saridakis, Ricci–Gauss–Bonnet holographic dark energy, Phys. Rev. D 97(6) (2018) 064035], a particular case of the most generalized [S. Nojiri, S. D. Odintsov and E. N. Saridakis, Modified cosmology from extended entropy with varying exponent, Eur. Phys. J. C 77 (2017) 528], encompassing its cosmological dynamics, thermodynamic behavior, and its realization within [Formula: see text] gravity. Using a spatially flat FRW background, we analyzed the Equation of State (EoS) parameter for three different interaction scenarios. The results revealed transitions between quintessence and phantom regimes. Stability was analyzed through squared speed of sound. From thermodynamic perspective, the Generalized Second Law of Thermodynamics (GSLT) was verified. The reconstructed [Formula: see text] model exhibited [Formula: see text] as [Formula: see text], ensuring recovery to general relativity at early times, while its late-time behavior drives accelerated expansion. The study demonstrates that the RGB-HDE framework provides a self consistent cosmological scenario unifying thermodynamic consistency with late time acceleration.