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1 Introduction

At high enough energies, Einstein’s theory of general relativity breaks down, and will be superceded by a quantum gravity theory. The classical singularities predicted by general relativity in gravitational collapse and in the hot big bang will be removed by quantum gravity. But even below the fundamental energy scale that marks the transition to quantum gravity, significant corrections to general relativity will arise. These corrections could have a major impact on the behaviour of gravitational collapse, black holes, and the early universe, and they could leave a trace – a “smoking gun” – in various observations and experiments. Thus it is important to estimate these corrections and develop tests for detecting them or ruling them out. In this way, quantum gravity can begin to be subject to testing by astrophysical and cosmological observations.

Developing a quantum theory of gravity and a unified theory of all the forces and particles of nature are the two main goals of current work in fundamental physics. There is as yet no generally accepted (pre-)quantum gravity theory. Two of the main contenders are M theory (for recent reviews see, e.g., [153, 263, 283]) and quantum geometry (loop quantum gravity; for recent reviews see, e.g., [272, 306]). It is important to explore the astrophysical and cosmological predictions of both these approaches. This review considers only models that arise within the framework of M theory, and mainly the 5-dimensional warped brane-worlds.

 1.1 Heuristics of higher-dimensional gravity
 1.2 Brane-worlds and M theory
 1.3 Heuristics of KK modes

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