Pauli-Fierz Gravitons on Friedmann-Robertson-Walker Background

TL;DR

This paper derives the Hamiltonian for massive gravitons on a FRW background, explores stability bounds, and analyzes scalar mode propagation speeds in a cosmological setting.

Contribution

It introduces a Hamiltonian formulation for Pauli-Fierz gravitons on FRW backgrounds and extends the Higuchi bound to cosmological scenarios.

Findings

Generalized the Higuchi bound to FRW backgrounds.

Found that the scalar mode speed is always less than light speed.

Identified limits on the graviton mass parameter.

Abstract

We derive the Hamiltonian describing Pauli-Fierz massive gravitons on a flat Friedmann-Robertson-Walker (FRW) cosmology in a particular, non-generic effective field theory. The cosmological evolution is driven by a scalar field Phi with an arbitrary potential V(Phi). The model contains two coupled scalar modes, corresponding to the fluctuations of Phi and to the propagating scalar component of the Pauli-Fierz graviton. In order to preserve the full gauge invariance of the massless version of the theory, both modes have to be taken into account. We canonically normalize the Hamiltonian and generalize the Higuchi bound to FRW backgrounds. We discuss how this bound can set limits on the value of the Pauli-Fierz mass parameter. We also observe that on a generic FRW background the speed of propagation of the scalar mode of the graviton is always smaller than the speed of light.