Hybrid Models in Loop Quantum Cosmology

TL;DR

This paper reviews the hybrid quantization approach in Loop Quantum Cosmology, which combines loop techniques for homogeneous sectors with quantum field methods for inhomogeneities, providing a framework for quantum cosmological models.

Contribution

It summarizes the development and applications of hybrid Loop Quantum Cosmology, highlighting its innovative combination of quantization methods for different sectors.

Findings

Hybrid approach effectively couples homogeneous and inhomogeneous sectors.

Applicable to Gowdy models and cosmological perturbations.

Provides a quantum framework capturing main geometric effects.

Abstract

In the framework of Loop Quantum Cosmology, inhomogeneous models are usually quantized by means of a hybrid approach that combines loop quantization techniques with standard quantum field theory methods. This approach is based on a splitting of the phase space in a homogeneous sector, formed by global, zero-modes, and an inhomogeneous sector, formed by the remaining, infinite number of modes, that describe the local degrees of freedom. Then, the hybrid quantization is attained by adopting a loop representation for the homogeneous gravitational sector, while a Fock representation is used for the inhomogeneities. The zero-mode of the Hamiltonian constraint operator couples the homogeneous and inhomogeneous sectors. The hybrid approach, therefore, is expected to provide a suitable quantum theory in regimes where the main quantum effects of the geometry are those affecting the zero-modes, while the inhomogeneities, still being quantum, can be treated in a more conventional way. This hybrid strategy was first proposed for the simplest cosmological midisuperspaces: the Gowdy models, and it has been later applied to the case of cosmological perturbations. This paper reviews the construction and main applications of hybrid Loop Quantum Cosmology