Inhomogeneous loop quantum cosmology: Hybrid quantization of the Gowdy model

Abstract

The Gowdy cosmologies provide a suitable arena to further develop Loop Quantum Cosmology, allowing the presence of inhomogeneities. For the particular case of Gowdy spacetimes with the spatial topology of a three-torus and a content of linearly polarized gravitational waves, we detail a hybrid quantum theory in which we combine a loop quantization of the degrees of freedom that parametrize the subfamily of homogeneous solutions, which represent Bianchi I spacetimes, and a Fock quantization of the inhomogeneities. Two different theories are constructed and compared, corresponding to two different schemes for the quantization of the Bianchi I model within the improved dynamics formalism of Loop Quantum Cosmology. One of these schemes has been recently put forward by Ashtekar and Wilson-Ewing. We address several issues including the quantum resolution of the cosmological singularity, the structure of the superselection sectors in the quantum system, or the construction of the Hilbert space of physical states.

Approximation methods in loop quantum cosmology: from Gowdy cosmologies to inhomogeneous models in Friedmann–Robertson–Walker geometries

“…This is a midisuperspace with three-torus spatial topology that contains inhomogeneities (corresponding to gravitational waves) varying in a single direction [26]. The quantization of this model has been carried out adopting a hybrid approach, which combines techniques of LQC when representing the homogeneous sector of the model with a Fock quantization of the inhomogeneities [27][28][29][30].…”

Loop quantum cosmology of a radiation-dominated flat FLRW universe

“…In all of these cases the big-bang singularity has also been shown to be replaced by a bounce. Space-times that allow anisotropies [11][12][13] and inhomogeneities (using a hybrid quantization procedure) [14,15] have also been studied in LQC; in the Bianchi and Gowdy models, the classical singularity is resolved as the singular states decouple from the non-singular states under the quantum dynamics. It is generally expected that the big-bang singularity is replaced by a bounce in this setting as well (see, e.g., studies of the effective equations for the LQC of the Bianchi I [16] and Gowdy [17] space-times), but this has not yet been shown as the full quantum dynamics have not yet been investigated.…”

“…The matter sector is usually dealt with in a perfunctory manner, although there do exist some studies on the polymeric matter sector in the literature [25,26] (including attempts to describe the perturbative degrees of freedom [27]). Most of the space-times studied to date in LQC are either vacuum space-times [12,14] or with the particularly simple choice of a massless scalar field [3, 5-7, 11, 13, 15]. While the cases of a massive scalar field in a flat FLRW space-time [28], and a vector field in the Bianchi I cosmology [29] have also been studied, a robust analysis of the dynamical sector of the theories at a genuinely quantum level has only been performed for matter choices (namely a massless scalar field or pressure-less dust) which are idealizations of realistic (from the point of view of particle physics) matter fields.…”

Modified FRW cosmologies arising from states of the hybrid quantum Gowdy model

“…We adopt a Schrödinger representation for the homogeneous massless scalar ϕ, a loop quantization for the Bianchi I degrees of freedom [6,13] within the so-called improved dynamics scheme [14], and a Fock representation for the nonzero modes of both gravitational and matter fields [15]. We will first deal with the representation of the Bianchi I sector.…”

“…Then, a loop quantization is adopted for the homogeneous degrees of freedom (which, in this way, fully retain the genuine quantum features of the space-time), while the inhomogeneous degrees of freedom are treated by means of a more conventional Fock quantization. This quantization strategy was applied for the first time to the case of the Gowdy cosmologies with linear polarization of the gravitational waves and with the spatial topology of a three-torus, T 3 , achieving a complete quantization of the model [5,6]. The study of these tractable cosmologies provides the opportunity to develop approximate methods and techniques to solve the complicated dynamics of inhomogeneous systems.…”