Quantum cosmology from three different perspectives

This introductory review is addressed to beginning researchers. Some of the distinguishing features of loop quantum gravity are illustrated through loop quantum cosmology of FRW models. In particular, these examples illustrate: i) how `emergent time' can arise; ii) how the technical issue of solving the Hamiltonian constraint and constructing the \emph{physical} sector of the theory can be handled; iii) how questions central to the Planck scale physics can be answered using s...

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 resear...

In the present article, which is the first part of a work in three parts, we build an equation of quantum gravity. This equation is tensorial, is equivalent to general relativity in vacuum, but differs completely from general relativity inside matter. This new equation possesses a dimensionless gravitational coupling constant, and passes all experimental tests that also passes general relativity. This quantum gravity and general relativity diverge essentially in the domain of...

Why is it interesting to try to understand the origin of the universe? Everything we observe today, including our existence, arose from that event. Although we still do not have a theory that allows us to describe the origin itself, the study of the very early era of the universe involves the ideal terrain to analyze the interface between two of today's most successful physical theories, General Relativity and Quantum physics. But it is also an area in which we have a large n...

Loop quantum gravity and cosmology are reviewed with an emphasis on evaluating the dynamics, rather than constructing it. The three crucial parts of such an analysis are (i) deriving effective equations, (ii) controlling the theory's microscopic degrees of freedom that lead to its spatial discreteness and refinement, and (iii) ensuring consistency and anomaly-freedom. All three issues are crucial for making the theory testable by conceptual and observational means, and they r...

Quantum cosmology in general denotes the application of quantum physics to the whole universe and thus gives rise to many realizations and examples, covering problems at different mathematical and conceptual levels. It is related to quantum gravity and more specifically describes the application to cosmological situations rather than the construction and analysis of quantum field equations. As there are several different approaches to quantum gravity, equations for quantum co...

An elementary review of quantum cosmology. (Talk given at Texas/Pascos 1992 at Berkeley)

The goal of this report is to provide an up to date account of results on the quantum nature of the big bang, obtained in loop quantum cosmology. They suggest a radical modification of the paradigm provided by general relativity for the issue of the Beginning. The article is addressed primarily to historians and philosophers of science.

This review presents an introduction to Quantum Cosmology, including the mathematical methods essential to the canonical approach, some of the existing conceptual problems and the connection of the models to possible observables.

Cosmological perturbations are generally described by quantum fields on (curved but) classical space-times. While this strategy has a large domain of validity, it can not be justified in the quantum gravity era where curvature and matter densities are of Planck scale. Using techniques from loop quantum gravity, the standard theory of cosmological perturbations is extended to overcome this limitation. The new framework sharpens conceptual issues by distinguishing between the t...