# The path integral measure, constraints and ghosts for massive gravitons with a cosmological constant

## TL;DR

This paper investigates the stability issues of massive gravity in de Sitter space using path integral methods, revealing that proper measure treatment and constraints can alter the known bounds on graviton mass.

## Contribution

It provides a path integral analysis of massive gravity with a cosmological constant, connecting stability bounds to the conformal factor problem and measure choices.

## Key findings

- Proper measure treatment can reverse the stability bound on graviton mass.
- The conformal factor problem influences stability analysis in massive gravity.
- Choice of DeWitt metric affects the stability conditions.

## Abstract

For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the conformal factor problem of Euclidean quantum (massless) gravity. When a constraint for massive gravity is incorporated and the proper treatment of the path integral measure is taken into account one finds that, for particular choices of the DeWitt metric on the space of metrics (in fact, the same choices as in the massless case), one obtains the opposite bound on the graviton mass.