Effective Lagrangian from Higher Curvature Terms: Absence of 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 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 highercurvature 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 the four-derivatives gravitation effectively explains, in addition to the usual massless graviton excitation, a massive spin-two and a massive scalar excitation. At tree-level, the massive spin-2 field is gauge independent but the massive scalar excitation is seen somehow gauge dependent, thus a gravitational action with four-derivative terms may have fewer than eight degrees of freedom and/or larger symmetry.