Time and Observables in Unimodular General Relativity

TL;DR

This paper introduces a cosmological time variable in unimodular gravity to measure the evolution of observables, identifying constants of motion on null hypersurfaces relative to this volume clock.

Contribution

It develops a Hamiltonian formulation of unimodular gravity with a new cosmological time variable and identifies constants of motion on null hypersurfaces.

Findings

A cosmological time variable is derived from the Hamiltonian formulation.

Constants of motion are identified on null hypersurfaces.

Evolution of observables is described with respect to the volume clock.

Abstract

A cosmological time variable is emerged from the hamiltonian formulation of unimodular theory of gravity to measure the evolution of dynamical observables in the theory. A set of constants of motion has been identified for the theory on the null hypersurfaces that its evolution is with respect to the volume clock introduced by the cosmological time variable.