Hybrid Loop Quantum Cosmology: An Overview

Abstract

Loop Quantum Gravity is a nonperturbative and background independent program for the quantization of General Relativity. Its underlying formalism has been applied successfully to the study of cosmological spacetimes, both to test the principles and techniques of the theory and to discuss its physical consequences. These applications have opened a new area of research known as Loop Quantum Cosmology. The hybrid approach addresses the quantization of cosmological systems that include fields. This proposal combines the description of a finite number of degrees of freedom using Loop Quantum Cosmology, typically corresponding to a homogeneous background, and a Fock quantization of the field content of the model. In this review we first present a summary of the foundations of homogeneous Loop Quantum Cosmology and we then revisit the hybrid quantization approach, applying it to the study of Gowdy spacetimes with linearly polarized gravitational waves on toroidal spatial sections, and to the analysis of cosmological perturbations in preinflationary and inflationary stages of the Universe. The main challenge is to extract predictions about quantum geometry effects that eventually might be confronted with cosmological observations. This is the first extensive review of the hybrid approach in the literature on Loop Quantum Cosmology.

Editorial: Loop Quantum Cosmology

“…This densitization parallels the standard one in LQG [1]. It has also been employed in different studies of homogeneous and isotropic cosmologies [12,41], and has been applied in recent works on nonrotating black holes [42,43]. This alternative lapse not only solves some of the problems encountered in Ref.…”

“…An even more appealing possibility is to introduce metric and/or matter perturbations in these quantum black holes, exploring if the system allows for transitions between black hole states and studying the evolution of the perturbations. This perturbed system could be treated using the hybrid formalism for LQC [12]. The ultimate idea would be to apply this kind of analysis to Hawking radiation (see e.g.…”

“…Taking N = |p c |p b N , with N the lapse function of the densitized constraint according to our previous comments, and adopting a factor ordering known as the MMO prescription [51], which has proven advantageous in the study of homogeneous and isotropic LQC [12], we then obtain the following operator representation for the Kantowski-Sachs contribution to the total Hamiltonian of the extended system (up to multiplication by N ):…”

“…Refs. [7][8][9][10][11][12][13][14]). In contrast, the application of LQG to the study of black hole spacetimes is not so firmly established yet, in spite of the considerable attention paid to this problem (for a far from exhaustive list of works on this issue, see Refs.…”

Quantization ambiguities and the robustness of effective descriptions of primordial perturbations in hybrid loop quantum cosmology

“…Nonetheless, the effective field equations that result for the cosmological perturbations with this strategy lead to a loss of hyperbolicity in high curvature regimes, and have been argued to produce a primordial power spectrum with enhanced short-scale correlations [36,37]. Our interest here is rather put on another approach to LQC, the so-called hybrid approach [17][18][19][20][21][22][23]38]. The corresponding effective description of the cosmological perturbations leads to very different physical results, compatible with the measurements of the cosmic microwave background (CMB) observations [39][40][41].…”