Late time cosmology in f(R, $G$) gravity with exponential interactions

Cosmological models with f(R) modified gravity are significant to investigate the present and late-time behavior of the Universe. The dynamics of the Universe is studied in the framework of f(R) = R + γR${}^2$ - λ ($\frac{R}{3m_s^2}$)${}^{\delta }$ gravity (γ , λ, δ are arbitrary constants) with a coupled Gauss-Bonnet (GB) term in the gravitational action and estimate the constraints on the model parameters as well as the late time behavior of the Universe. In this case, the coupled Gauss-Bonnet term is coupled with a free scalar field in the presence of interacting fluid. In addition, we investigate the same for a different form of gravity f(R) = R, where the coupled GB term is coupled with a scalar field in a self-interacting potential.