Dynamics of Dirac observables in canonical cosmological perturbation theory

Abstract

The relational formalism based on geometrical clocks and Dirac observables in linearized canonical cosmological perturbation theory is used to introduce an efficient method to find evolution equations for gauge invariant variables. Our method generalizes an existing technique by Pons, Salisbury and Sundermeyer [1, 2] to relate the evolution of gauge invariant observables with the one of gauge variant quantities, and is applied as a demonstration for the longitudinal and spatially flat gauges. Gauge invariant evolution equations for the Bardeen potential and the Mukhanov-Sasaki variable are derived in the extended ADM phase space. Our method establishes a full agreement at the dynamical level between the canonical and conventional cosmological perturbation theory at the linear order using Dirac observables.

arXiv comment43 pages, appendix on Dirac observables in perturbation theory added. To appear in Class. Quant. Grav

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• Relating dust reference models to conventional systems in manifestly gauge invariant perturbation theory
• Cosmological perturbation theory with matter time
• Loop Quantum Cosmology: Physics of Singularity Resolution and its Implications
• Alternative effective mass functions in the modified Mukhanov-Sasaki equation of loop quantum cosmology
• Geometrical Quantum Time in the $U(1{)}^3$ Model of Euclidean Quantum Gravity