Cosmological scaling solutions in generalised Gauss--Bonnet gravity theories

The conditions for the existence and stability of cosmological power-law scaling solutions are established when the Einstein–Hilbert action is modified by the inclusion of a function of the Gauss–Bonnet curvature invariant. The general form of the action that leads to such solutions is determined for the case where the universe is sourced by a barotropic perfect fluid. It is shown by employing an equivalence between the Gauss–Bonnet action and a scalar–tensor theory of gravity that the cosmological field equations can be written as a plane autonomous system. It is found that stable scaling solutions exist when the parameters of the model take appropriate values.