Avoiding the cosmological constant issue in a class of phenomenologically viable $F(R,{\cal G})$ theories

In this paper we investigate a class of phenomenologically viable $F(R,{\cal G})$ theories that are able to avoid the cosmological constant issue. While the absence of ghosts and other kinds of instability issues is of prime importance, other reasonable requirements such as vanishing effective (low curvature) cosmological constant, including the flat space as a stable vacuum solution, are also imposed on the viable models. These are free of the cosmological constant problem thanks to the following outstanding feature: the de Sitter space is an attractor of the asymptotic cosmological dynamics, with the resulting constant Hubble rate being unrelated both to the energy density of vacuum and to the low-curvature effective cosmological constant.