Pauli-Fierz Gravitons on Friedmann-Robertson-Walker Background

TL;DR

Grisa and Sorbo derive a canonical Hamiltonian for Pauli-Fierz massive gravitons on a flat FRW background driven by a scalar field with arbitrary potential $V(\Phi)$. The analysis reveals two coupled scalar modes, with a generalized Higuchi bound $\nu^2>0$, where $\nu^2 = m^2 - 2H^2 - 2\dot{H}$, and identifies a stronger gradient bound $m^2 > (1 - w)H^2$ that ensures stability and subluminal propagation of the scalar graviton mode, whose velocity is $v_s = \sqrt{1 + \tfrac{4\dot{H}}{3\nu^2}}$ for $\dot{H}<0$. Tensor and vector sectors are shown to be well-behaved after canonical normalization, while the scalar sector carries Lorentz-violating dispersion due to the FRW background. The work provides a framework for constraining the PF graviton mass in cosmology and discusses implications for infrared modifications of gravity, vDVZ, and strong coupling within an effective field theory context.

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.