Time and Dirac Observables in Friedmann Cosmologies

TL;DR

This paper introduces a cosmological time variable in Friedmann models derived from Hamiltonian formulation, enabling the measurement of dynamical observables' evolution with respect to a volume clock.

Contribution

It presents a novel Hamiltonian-based approach to defining a cosmological time and identifies observables evolving with respect to this volume clock.

Findings

A cosmological time variable is derived from the Hamiltonian formulation.

A set of observables on null hypersurfaces is identified.

The evolution of these observables is described with respect to the volume clock.

Abstract

A cosmological time variable is emerged from the Hamiltonian formulation of Friedmann model to measure the evolution of dynamical observables in the theory. A set of observables 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.