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In this paper we investigate a class of phenomenologically viable $F(R,{\calG})$ theories that are able to avoid the cosmological constant issue. While theabsence 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 cosmologicalconstant problem thanks to the following outstanding feature: the de Sitterspace is an attractor of the asymptotic cosmological dynamics, with theresulting constant Hubble rate being unrelated both to the energy density ofvacuum and to the low-curvature effective cosmological constant.

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