Viable singularity-free f(R) gravity without a cosmological constant

Several authors have argued that self-consistent f(R) gravity models distinct from the cold dark matter model with a cosmological constant (LambdaCDM) are almost ruled out. Confronting such claims, we present a particular two-parameter f(R) model that (a) is cosmologically viable and distinguishable from LambdaCDM, (b) is compatible with the existence of relativistic stars, (c) is free of singularities of the Ricci scalar during the cosmological evolution, and (d) allows the addition of high-curvature corrections that could be relevant for inflation.