Dynamics of Dirac observables in canonical cosmological perturbation theory

Giesel, Kristina; Singh, Parampreet; Winnekens, David

doi:10.1088/1361-6382/ab0ed3

Cited by 16 publications

(11 citation statements)

References 35 publications

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“…An aspect where this issue becomes immediately relevant is for instance when one derives the gauge invariant dynamics of for instance the Bardeen potential and the Mukhanov-Sasaki variable in linear perturbation theory. In contrast to the conventional way, this dynamics can be obtained in a very straightforward and efficient way in our formalism [41]. This occurs thanks to the implementation of the gauge invariance of the first kind in our formalism which allows one to derive the dynamics of these gauge invariant quantities purely at the gauge invariant level without the need to go back to the gauge variant form of the Einstein equations and derive from it the associated dynamics of the observables.…”

Section: F Generalized Gauge Fixing Constraints and Modified Gaugesmentioning

confidence: 99%

Gauge invariant variables for cosmological perturbation theory using geometrical clocks

Giesel

Herzog

Singh

2018

Class. Quantum Grav.

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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.

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Section: F Generalized Gauge Fixing Constraints and Modified Gaugesmentioning

confidence: 99%

Gauge invariant variables for cosmological perturbation theory using geometrical clocks

Giesel

Herzog

Singh

2018

Class. Quantum Grav.

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“…Furthermore, when the test-field approximation is employed, in which the background quantum states are 1 Existence of such a phase is not confined to FLRW models but also exists even with standard loop quantization in certain anisotropic spacetimes [28]. 2 This restriction can be lifted in the extended phase space where a generalization of Langlois' treatment has been recently found which allows construction of gauge-invariant variables other than the Mukhanov-Sasaki variable in canonical theory [54,55]. 3 A treatment similar to Langlois' analysis for Bianchi-I spacetimes has been carried out in [56].…”

Section: Introductionmentioning

confidence: 99%

Primordial power spectrum from the dressed metric approach in loop cosmologies

Singh

Wang

2020

Phys. Rev. D

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We investigate the consequences of different regularizations and ambiguities in loop cosmological models on the predictions in the scalar and tensor primordial spectrum of the cosmic microwave background using the dressed metric approach. Three models, standard loop quantum cosmology (LQC), and two modified loop quantum cosmologies (mLQC-I and mLQC-II) arising from different regularizations of the Lorentzian term in the classical Hamiltonian constraint are explored for chaotic inflation in spatially-flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. In each model, two different treatments of the conjugate momentum of the scale factor are considered. The first one corresponds to the conventional treatment in dressed metric approach, and the second one is inspired from the hybrid approach which uses the effective Hamiltonian constraint. For these two choices, we find the power spectrum to be scale-invariant in the ultra-violet regime for all three models, but there is at least a 10% relative difference in amplitude in the infra-red and intermediate regimes. All three models result in significant differences in the latter regimes. In mLQC-I, the magnitude of the power spectrum in the infra-red regime is of the order of Planck scale irrespective of the ambiguity in conjugate momentum of the scale factor. The relative difference in the amplitude of the power spectrum between LQC and mLQC-II can be as large as 50% throughout the infra-red and intermediate regimes. Differences in amplitude due to regularizations and ambiguities turn out to be small in the ultra-violet regime.arXiv:1912.08225v2 [gr-qc]

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“…where the last equality follows from (13). Thus the physical Hamiltonian is determined up to an overall sign of the lapse function.…”

Section: A Dust Time Gaugementioning

confidence: 99%

“…Our work is not the first to construct a hamiltonian perturbation theory for cosmology. The first such analysis was given in [12]; others using the relational approach have appeared recently [13,14]. However our approach differs from both in several respects, the primary one being that we use only a clock field, and fix a matter-time gauge strongly at the outset before proceeding to cosmology [7].…”

Section: Introductionmentioning

confidence: 99%

Cosmological perturbation theory with matter time

Husain,

Saeed

2020

Preprint

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We study cosmological perturbation theory with scalar field and pressureless dust in the Hamiltonian formulation, with the dust field chosen as a matter-time gauge. The corresponding canonical action describes the dynamics of the scalar field and metric degrees of freedom with a non-vanishing physical Hamiltonian and spatial diffeomorphism constraint. We construct a momentum space Hamiltonian that describes linear perturbations, and show that the constraints to this order form a first class system. We then write the Hamiltonian as a function of certain gauge invariant canonical variables and show that it takes the form of an oscillator with time dependent mass and frequency coupled to an ultralocal field. We compare our analysis with other Hamiltonian approaches to cosmological perturbation theory that do not use dust time.

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Dynamics of Dirac observables in canonical cosmological perturbation theory

Cited by 16 publications

References 35 publications

Gauge invariant variables for cosmological perturbation theory using geometrical clocks

Gauge invariant variables for cosmological perturbation theory using geometrical clocks

Primordial power spectrum from the dressed metric approach in loop cosmologies

Cosmological perturbation theory with matter time

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