Cosmological expansion problem and the nature of entropy in extended Gauss-Bonnet gravity

In this study, we mainly focus on cosmological entropy law of thermodynamics in Gauss-Bonnet gravity and we construct the generalized second law (GSL) of thermodynamics for this theory on the dynamical apparent and event horizons. First, we find the exact scale factor power law solutions of the field equations by assuming the lagrangian density is given as R+f(G)+〖αR〗^2. Three evolutionary stages of our universe has been determined mathematically in a unified form. Next, we investigated the scale factor power law solutions of the corresponding field equation of F(R,G) gravity by determining F(R,G) 〖=f〗_1 (G)+f_2 (R). After constructing GSL on the apparent and event horizons and applying corresponding solutions to the law, we analyzed evolutionary stages of the Universe in detail.