Partial Masslessness and Conformal Gravity

Understand

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 gravitational- and self- interactions 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.