Generalized massive gravity in arbitrary dimensions and its Hamiltonian formulation

TL;DR

This paper generalizes the dRGT massive gravity model to arbitrary dimensions with multiple scalars, deriving its Hamiltonian formulation and analyzing ghost instabilities in different sectors.

Contribution

It introduces a Hamiltonian formulation for a generalized scalar massive-tensor theory in arbitrary dimensions, extending previous models and analyzing ghost constraints.

Findings

Two sectors identified: general and special.

Ghosts are eliminated in both sectors except in the special sector with more than two dimensions.

A second BD ghost appears in the special sector with one scalar.

Abstract

We extend the four-dimensional de Rham-Gabadadze-Tolley (dRGT) massive gravity model to a general scalar massive-tensor theory in arbitrary dimensions, coupling a dRGT massive graviton to multiple scalars and allowing for generic kinetic and mass matrix mixing between the massive graviton and the scalars, and derive its Hamiltonian formulation and associated constraint system. When passing to the Hamiltonian formulation, two different sectors arise: a general sector and a special sector. Although obtained via different ways, there are two second class constraints in either of the two sectors, eliminating the BD ghost. However, for the special sector, there are still ghost instabilities except for the case of two dimensions. In particular, for the special sector with one scalar, there is a "second BD ghost".