In this work, the Gauss-Bonnet model of modified gravity is investigated, where some arbitrary function G is added to the Einstein-Hilbert action. This theory explains the accelerated expansion of the Universe. In this work. The article proposes F(R, G) = f(R) + η(G) modified gravity, which considers two gravities f(R) and η(G), where f(R) is a function from the Ricci scalar, ...