Gauge invariant variables for cosmological perturbation theory using geometrical clocks

Abstract

Using the extended ADM-phase space formulation in the canonical framework we analyze the relationship between various gauge choices made in cosmological perturbation theory and the choice of geometrical clocks in the relational formalism. We show that various gauge invariant variables obtained in the conventional analysis of cosmological perturbation theory correspond to Dirac observables tied to a specific choice of geometrical clocks. As examples, we show that the Bardeen potentials and the Mukhanov-Sasaki variable emerge naturally in our analysis as observables when gauge fixing conditions are determined via clocks in the Hamiltonian framework. Similarly other gauge invariant variables for various gauges can be systematically obtained. We demonstrate this by analyzing five common gauge choices: longitudinal, spatially flat, uniform field, synchronous and comoving gauge. For all these, we apply the observable map in the context of the relational formalism and obtain the corresponding Dirac observables associated with these choices of clocks. At the linear order, our analysis generalizes the existing results in canonical cosmological perturbation theory twofold. On the one hand we can include also gauges that can only be analyzed in the context of the extended ADM-phase space and furthermore, we obtain a set of natural gauge invariant variables, namely the Dirac observables, for each considered choice of gauge conditions. Our analysis provides insights on which clocks should be used to extract the relevant natural physical observables both at the classical and quantum level. We also discuss how to generalize our analysis in a straightforward way to higher orders in the perturbation theory to understand gauge conditions and the construction of gauge invariant quantities beyond linear order.

arXiv commentDiscussion expanded, references added. To appear in Classical and Quantum Gravity

References in corpus (21)

• Partial observables
• Partial and Complete Observables for Hamiltonian Constrained Systems
• Partial and Complete Observables for Canonical General Relativity
• Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories
• Gravity quantized
• Scalar Material Reference Systems and Loop Quantum Gravity
• Reduced Phase Space Quantization and Dirac Observables
• Evolution of non-linear cosmological perturbations
• Nonlinear perturbations of cosmological scalar fields
• Revisiting observables in generally covariant theories in the light of gauge fixing methods
• A perturbative approach to Dirac observables and their space-time algebra
• Hamiltonian cosmological perturbation theory with loop quantum gravity corrections
• Formation and Evolution of Structure in Loop Cosmology
• Gauge dependence in the theory of non-linear spacetime perturbations
• Conserved cosmological structures in the one-loop superstring effective action
• Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology
• Observables and gauge invariance in the theory of non-linear spacetime perturbations
• Dust reference frame in quantum cosmology
• Hamiltonian approach to 2nd order gauge invariant cosmological perturbations
• Rigid and gauge Noether symmetries for constrained systems
• Gauge invariant canonical cosmological perturbation theory with geometrical clocks in extended phase space - a review and applications

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