Effective Lagrangian from higher-curvature terms: absence of a vDVZ discontinuity in AdS space

We demonstrate that the van Dam-Veltman-Zakharov discontinuity arising in the M² \→ 0 limit of the massive graviton through an explicit Pauli-Fierz mass term is special to Minkowski space, and it is absent in anti de Sitter space, in particular, when graviton acquires mass spontaneously from the higher curvature terms. More generally, the massless limit M²\→ 0 is attained faster than the cosmological constant \Λ \→ 0, and the absence of discontinuity may persist up to the quantum level. We discuss the effects of higher-curvature couplings and of an explicit cosmological term (\Λ) on stability of such continuity and of massive excitations. We also confirm the earlier assertion by Stelle that four-derivative gravity effectively contains, in addition to the usual massless graviton excitation, a massive spin-two and a massive scalar excitations. At tree-level, the massive spin-2 field is gauge independent, but the massive scalar excitation is seen somehow gauge dependent, thus the gravitational action with the four-derivative terms may have fewer than eight degrees of freedom and/or larger symmetry.