Effective Field Theory for Massive Gravitons and Gravity in Theory Space

TL;DR

This paper develops a formalism to restore coordinate invariance in theories with massive gravitons, clarifying their properties, effective field theory limits, and nonlinear effects, enabling new approaches in gravity model building.

Contribution

It introduces a gauge-invariance restoring technique for massive gravity theories, providing a clearer understanding of their effective field theories and nonlinear behaviors.

Findings

Effective field theory valid up to a high-energy cutoff Lambda.

Cutoff scales depend on graviton mass and Planck scale, with specific formulas.

Clarification of nonlinear effects and the Fierz-Pauli form necessity.

Abstract

We introduce a technique for restoring general coordinate invariance into theories where it is explicitly broken. This is the analog for gravity of the Callan-Coleman-Wess-Zumino formalism for gauge theories. We use this to elucidate the properties of interacting massless and massive gravitons. For a single graviton with a Planck scale Mpl and a mass mg, we find that there is a sensible effective field theory which is valid up to a high-energy cutoff Lambda parametrically above mg. Our methods allow for a transparent understanding of the many peculiarities associated with massive gravitons, among them the need for the Fierz-Pauli form of the Lagrangian, the presence or absence of the van Dam-Veltman-Zakharov discontinuity in general backgrounds, and the onset of non-linear effects and the breakdown of the effective theory at large distances from heavy sources. The natural sizes of all non-linear corrections beyond the Fierz-Pauli term are easily determined. The cutoff scales as Lambda ~ (mg^4 Mpl)^(1/5) for the Fierz-Pauli theory, but can be raised to Lambda ~ (mg^2 Mpl)^(1/3) in certain non-linear extensions. Having established that these models make sense as effective theories, there are a number of new avenues for exploration, including model building with gravity in theory space and constructing gravitational dimensions.