Generalized second law of thermodynamics on the apparent horizon in modified Gauss-Bonnet gravity

Modified gravity and generalized second law (GSL) of thermodynamics are interesting topics in the modern cosmology. In this regard, we investigate the GSL of gravitational thermodynamics in the framework of modified Gauss-Bonnet gravity or f(G)-gravity. We consider a spatially FRW universe filled with the matter and radiation enclosed by the dynamical apparent horizon with the Hawking temperature. For two viable f(G) models, we first numerically solve the set of differential equations governing the dynamics of f(G)-gravity. Then, we obtain the evolutions of the Hubble parameter, the Gauss-Bonnet curvature invariant term, the density and equation of state parameters as well as the deceleration parameter. In addition, we check the energy conditions for both models and finally examine the validity of the GSL. For the selected f(G) models, we conclude that both models have a stable de Sitter attractor. The equation of state parameters behave quite similar to those of the LCDM model in the radiation/matter dominated epochs, then they enter the phantom region before reaching the de Sitter attractor with w=-1. The deceleration parameter starts from the radiation/matter dominated eras, then transits from a cosmic deceleration to acceleration and finally approaches a de Sitter regime at late times, as expected. Furthermore, the GSL is respected for both models during the standard radiation/matter dominated epochs. Thereafter when the universe becomes accelerating, the GSL is violated in some ranges of scale factor. At late times, the evolution of the GSL predicts an adiabatic behavior for the accelerated expansion of the universe.