Partial Masslessness and Conformal Gravity

We use conformal, but ghostful, Weyl gravity to study its ghost-free, second derivative, partially massless (PM) spin 2 component in presence of Einstein gravity with positive cosmological constant. Specifically, we consider both gravitationaland selfinteractions of PM via the fully non-linear factorization of conformal gravity’s Bach tensor into Einstein times Schouten operators. We find that extending PM beyond linear order suffers from familiar higher-spin consistency obstructions: it propagates only in Einstein backgrounds, and the conformal gravity route generates only the usual safe, Noether, cubic order vertices. PACS: 04.62.+v, 04.50.-h, 04.50.Kd, 04.62.+v, 02.40.-k