Linearized gravity with matter time

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.

arXiv comment10 pages (references added)

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• Mukhanov-Sasaki equation in manifestly gauge-invariant linearized cosmological perturbation theory with dust reference fields
• The Universe as an Oscillator
• Relating dust reference models to conventional systems in manifestly gauge invariant perturbation theory
• Cosmological perturbation theory with matter time
• Physical Hamiltonian for mimetic gravity
• Isotropic stellar model in mimetic theory