A brief introduction to Loop Quantum Cosmology

Abstract

In recent years, Loop Quantum Gravity has emerged as a solid candidate for a nonperturbative quantum theory of General Relativity. It is a background independent theory based on a description of the gravitational field in terms of holonomies and fluxes. In order to discuss its physical implications, a lot of attention has been paid to the application of the quantization techniques of Loop Quantum Gravity to symmetry reduced models with cosmological solutions, a line of research that has been called Loop Quantum Cosmology. We summarize its fundamentals and the main differences with respect to the more conventional quantization approaches employed in cosmology until now. In addition, we comment on the most important results that have been obtained in Loop Quantum Cosmology by analyzing simple homogeneous and isotropic models. These results include the resolution of the classical big-bang singularity, which is replaced by a quantum bounce.

Introduction to Loop Quantum Cosmology

“…LQC [2,4,44,149] adapts the techniques developed in loop quantum gravity [14,170,186] to the quantization of simpler models than the full theory, as minisuperspace models. Minisuperspace models are solutions of Einstein's equations with a high degree of symmetry, so much so that there are no field theory degrees of freedom remaining.…”

Time-dependent mass of cosmological perturbations in the hybrid and dressed metric approaches to loop quantum cosmology

“…This is a nonperturbative canonical quantization of GR which, in a background-independent way, adopts the strategy followed by Yang-Mills theories, adapted to the description of the gravitational degrees of freedom [6]. With an eye on possible tests of the physical consequences that this nonperturbative quantization implies, the techniques of LQG have been applied to cosmological spacetimes, giving rise to a field of research known as loop quantum cosmology (LQC) [7][8][9][10]. One of the most remarkable results reached for homogeneous spacetimes in LQC is the, quite generic, quantum resolution of the big bang singularity, which becomes what has been named as big bounce [9,11].…”

Editorial: Loop Quantum Cosmology

“…Loop Quantum Gravity (LQG) is one of the most solid candidates for a quantum theory of General Relativity (GR) [1,2]. LQG techniques have been extensively applied to cosmological studies [3][4][5][6], giving rise to the discipline known as Loop Quantum Cosmology (LQC). High curvature scenarios, such as the Early Universe or black holes, are crucial for testing quantum gravity, as its effects are expected to become significant in these situations.…”

“…High curvature scenarios, such as the Early Universe or black holes, are crucial for testing quantum gravity, as its effects are expected to become significant in these situations. In this context, LQC has successfully been used to investigate a variety of cosmological models, both isotropic and anisotropic, with and without matter content, and with and without spatial curvature [3,4]. It has also led to predictions about the effects of LQG on the primordial spectra of cosmological perturbations (see e.g.…”