New Branches of Massive Gravity

Understand

The basic building block for Lorentz invariant and ghost free massive gravity is the square root of the combination $g^{-1}\eta\,$, where $g^{-1}$ is the inverse of the physical metric and $\eta$ is a reference metric.

• Since the square root of a matrix is not uniquely defined, it is possible to have physically inequivalent potentials corresponding to different branches.
• We show that around Minkowski background the only perturbatively well defined branch is the potential proposed by de Rham, Gabadadze and Tolley.
• On the other hand, if Lorentz symmetry is broken spontaneously, other potentials exist with a standard perturbative expansion.