Quantum gravity is expected to be necessary in order to understand situations where 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 space-time 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 space-time is then modified. One particular realization 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. Main effects are introduced into effective classical equations which allow to avoid 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 to extend space-time 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 space-time arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time. ELECTRONIC SUPPLEMENTARY MATERIAL Supplementary material is available for this article at 10.12942/lrr-2005-11.

中文翻译：

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循环量子宇宙学。

为了理解经典广义相对论失效的情况，预计量子引力是必要的。特别是在宇宙学中，人们必须处理初始奇点，即经典时空的向后演化不可避免地在有限的适当时间之后结束的事实。这呈现了对经典图景的分解，并且需要扩展的理论来进行有意义的描述。由于涉及小长度尺度和高曲率，因此量子效应必须发挥作用。不仅奇点本身，而且周围的时空也会被修改。一个特殊的实现是环量子宇宙学，这是环量子引力在均匀系统中的应用，它消除了经典奇点。其影响可以在不同层面上进行研究。主效应被引入有效的经典方程中，从而避免了量子理论的解释问题。它们催生了新型早期宇宙现象学，并应用于暴胀和循环模型。为了解决经典奇点并理解它们周围的几何结构，量子描述是必要的。然后，经典演化被波函数的差分方程所取代，该方程允许将时空扩展到经典奇点之外。一个主要问题是这些同质场景如何与全环量子引力相关，这可以在分布对称态的水平上进行处理。最后，圈量子引力中出现的新时空结构及其在宇宙学中的应用为时间等更普遍的问题提供了新的线索。电子补充材料 本文的补充材料可在 10.12942/lrr-2005-11 上找到。