Linearized gravity with matter time

TL;DR

This paper analyzes linearized general relativity with pressureless dust as a matter-time gauge, revealing covariant graviton modes and an ultralocal scalar mode, with modifications affecting the scalar's propagation speed.

Contribution

It introduces a canonical formulation of gravity with dust as a matter-time gauge and explores the properties of graviton and scalar modes, including a deformation parameter's effects.

Findings

Graviton modes remain Lorentz covariant despite the gauge.

Scalar mode is ultralocal in the original theory.

Deformation parameter introduces scalar mode propagation.

Abstract

We study general relativity with pressureless dust in the canonical formulation, with the dust field chosen as a matter-time gauge. The resulting theory has three physical degrees of freedom in the metric field. The linearized canonical theory reveals two graviton modes and a scalar mode. We find that the graviton modes remain Lorentz covariant despite the time gauge, and that the scalar mode is ultralocal. We discuss also a modification of the theory to include a parameter in the Hamiltonian analogous to that in Horava-Lifshitz models. In this case the scalar mode is no longer ultralocal, and acquires a propagation speed dependent on the deformation parameter.