Scalar and Vector Perturbations in Quantum Cosmological Backgrounds

Abstract

Generalizing a previous work concerning cosmological linear tensor perturbations, we show that the lagrangians and hamiltonians of cosmological linear scalar and vector perturbations can be put in simple form through the implementation of canonical transformations and redefinitions of the lapse function, without ever using the background classical equations of motion. In particular, if the matter content of the Universe is a perfect fluid, the hamiltonian of scalar perturbations can be reduced, as usual, to a hamiltonian of a scalar field with variable mass depending on background functions, independently of the fact that these functions satisfy the background Einstein's classical equations. These simple lagrangians and hamiltonians can then be used in situations where the background metric is also quantized, hence providing a substantial simplification over the direct approach originally developed by Halliwell and Hawking.

19 pages, no figure

References in corpus (29)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• The Ekpyrotic Universe: Colliding Branes and the Origin of the Hot Big Bang
• Pre-Big-Bang in String Cosmology
• Quantum Nature of the Big Bang
• Superstring Cosmology
• On the Generation of a Scale-Invariant Spectrum of Adiabatic Fluctuations in Cosmological Models with a Contracting Phase
• Quantum cosmological perfect fluid models
• The Causal Interpretation of Dust and Radiation Fluids Non-Singular Quantum Cosmologies
• Primordial perturbations in a non singular bouncing universe model
• Cosmological perturbations through a simple bounce
• Passing through the bounce in the ekpyrotic models
• A non inflationary model with scale invariant cosmological perturbations
• Perturbations in a non-singular bouncing Universe
• Ostrogradski Formalism for Higher-Derivative Scalar Field Theories
• Tensor Perturbations in Quantum Cosmological Backgrounds
• Radiation-Dominated Quantum Friedmann Models
• Gaussian superpositions in scalar-tensor quantum cosmological models
• Cosmological perturbations and the transition from contraction to expansion
• On the "Causality Argument" in Bouncing Cosmologies
• Visible Branes with Negative Tension in Heterotic M-Theory
• Has the Universe always expanded ?
• Study of a Class of Four Dimensional Nonsingular Cosmological Bounces
• Gravitational wave background in perfect fluid quantum cosmologies
• Regular two-component bouncing cosmologies and perturbations therein
• Regular cosmological solutions in low energy effective action from string theories
• Adiabatic and entropy perturbations propagation in a bouncing Universe
• General solution for scalar perturbations in bouncing cosmologies
• A Note on Perturbations During a Regular Bounce
• The Isaacson expansion in quantum cosmology

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• Hybrid Loop Quantum Cosmology: An Overview
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• Time-dependent mass of cosmological perturbations in the hybrid and dressed metric approaches to loop quantum cosmology
• An Inflationary Non-singular Quantum Cosmological Model
• Consistent Scalar and Tensor Perturbation Power Spectra in Single Fluid Matter Bounce with Dark Energy Era
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• Non-oscillating power spectra in Loop Quantum Cosmology
• Bouncing models with a cosmological constant
• Quantum Cosmological Perturbations of Generic Fluids in Quantum Universes
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• Gauge invariant canonical cosmological perturbation theory with geometrical clocks in extended phase space - a review and applications
• Scalar Field Perturbations with Arbitrary Potentials in Quantum Backgrounds
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• The simplest possible bouncing quantum cosmological model
• Perturbations in Quantum Cosmology: The Continuum Limit in Fourier Space
• Hamiltonian formalism and gauge-fixing conditions for cosmological perturbation theory
• Vector perturbations in bouncing cosmology
• Large classical universes emerging from quantum cosmology
• Stochastic background of relic gravitons in a bouncing quantum cosmological model
• A model of quantum collapse induced by gravity
• Non-Gaussianities as a Signature of Quantumness of Quantum Cosmology
• A Momentous Arrow of Time
• Quantum entanglement and non-Gaussianity in the primordial Universe
• Quantum collapse dynamics with attractive densities
• Will quantum cosmology resurrect chaotic inflation model?
• Radiation-dominated bouncing model with slow contraction and inflation
• Primordial perturbations in kinetically dominated regimes of general relativity and hybrid quantum cosmology
• Gravitational quantum collapse in dilute systems
• Non-oscillating vacuum states and the quantum homogeneity and isotropy hypothesis in Loop Quantum Cosmology