Abstract
Quantum gravity is expected to be necessary in order to understand situations in which classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical spacetime inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding spacetime is then modified. One particular theory is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. The main effects are introduced into effective classical equations, which allow one to avoid the interpretational problems of quantum theory. They give rise to new kinds of early-universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function, which allows an extension of quantum spacetime beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of spacetime arising in loop quantum gravity and its application to cosmology sheds light on more general issues, such as the nature of time.Electronic Supplementary MaterialSupplementary material is available for this article at 10.12942/lrr-2008-4.
Highlights
Living Reviews in Relativity is a peer reviewed open access journal published by the Max Planck Institute for Gravitational Physics, Am Muhlenberg 1, 14476 Potsdam, Germany
Loop cosmology is a phenomenological description of quantum effects in cosmology, obtained in the framework of a background independent and non-perturbative quantization
Quantum backreaction has not yet been studied systematically except for special models. These corrections are responsible for a surprising variety of phenomena, which all improve the behavior in classical cosmology
Summary
While general relativity is very successful in describing gravitational interaction and the structure of space and time on large scales [308], quantum gravity is needed for small-scale behavior. This is usually relevant when curvature, or in physical terms energy densities and tidal forces, becomes large. Rather than dealing with a classical spacetime manifold, we have evolution equations for the wave function of a universe This opens up a vast number of problems on various levels from mathematical physics to cosmological observations, and even philosophy. This review is intended to give an overview and summary of the current status of those problems, in particular in the new framework of loop quantum cosmology
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