Approximation methods in Loop Quantum Cosmology: From Gowdy cosmologies to inhomogeneous models in Friedmann-Robertson-Walker geometries

Abstract

We develop approximation methods in the hybrid quantization of the Gowdy model with linear polarization and a massless scalar field, for the case of three-torus spatial topology. The loop quantization of the homogeneous gravitational sector of the Gowdy model (according to the improved dynamics prescription) and the presence of inhomogeneities lead to a very complicated Hamiltonian constraint. Therefore, the extraction of physical results calls for the introduction of well justified approximations. We first show how to approximate the homogeneous part of the Hamiltonian constraint, corresponding to Bianchi I geometries, as if it described a Friedmann-Robertson-Walker (FRW) model corrected with anisotropies. This approximation is valid in the high-energy sector of the FRW geometry (concerning its contribution to the constraint) and for anisotropy profiles that are sufficiently smooth. In addition, for certain families of states associated to regimes of physical interest, with negligible effects of the anisotropies and small inhomogeneities, one can approximate the Hamiltonian constraint of the inhomogeneous system by that of an FRW geometry with a relatively simple matter content, and then obtain its solutions.

20 pages, 3 figures. Minor changes, matches published version

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Cited by in corpus (12)

• Cosmological perturbations in Hybrid Loop Quantum Cosmology: Mukhanov-Sasaki variables
• Primordial power spectra for scalar perturbations in loop quantum cosmology
• Hybrid loop quantum cosmology and predictions for the cosmic microwave background
• On effective loop quantum geometry of Schwarzschild interior
• Hybrid Loop Quantum Cosmology: An Overview
• Quantum corrections to the Mukhanov-Sasaki equations
• Hybrid Models in Loop Quantum Cosmology
• Loop quantization of the Gowdy model with local rotational symmetry
• Separable Hilbert space for loop quantization
• Modified FRW cosmologies arising from states of the hybrid quantum Gowdy model
• Modeling effective FRW cosmologies with perfect fluids from states of the hybrid quantum Gowdy model
• Inflation from inhomogeneous polarized Gowdy model