General Vacuum Solution of Modified Gravity with Gauss–Bonnet Term

We present a general vacuum solution of the modified Gauss–Bonnet gravity equations for the Friedmann–Lemaître–Robertson–Walker metric. We use an ansatz to reduce the gravitational equations to an ordinary differential equation for the function \(F=F(G)\) . The solution obtained depends on an arbitrary function and is new. As an example, we take the arbitrary function in the form of a power one and analyze the solutions for both \(F(G)\) and the main cosmological physical quantities as the scale factor, Hubble rate, the Gauss–Bonnet term and the scalar curvature.