At high enough energies, Einstein’s theory of general relativity breaks down, and will be superceded by a quantum gravity theory.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 reviews see, e.g., [214, 356, 377]) and quantum geometry (loop quantum gravity; for reviews see, e.g., [365, 409]). 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.

In this review, we focus on RS brane-worlds (mainly the RS 1-brane model) and their generalizations, with the emphasis on geometry and gravitational dynamics (see [304, 314, 269, 424, 348, 268, 360, 120, 49, 267, 270] for previous reviews with a broadly similar approach). Other reviews focus on string-theory aspects, e.g., [147, 316, 97, 357], or on particle physics aspects, e.g., [354, 366, 261, 151, 75]. We also discuss the 5D DGP models, which modify general relativity at low energies, unlike the RS models; these models have become important examples in cosmology for achieving late-time acceleration of the universe without dark energy. Finally, we give brief overviews of 6D models, in which the brane has co-dimension two, introducing very different features to the 5D case with co-dimension one branes. Update

1.1 Heuristics of higher-dimensional gravity

1.2 Brane-worlds and M theory

1.3 Heuristics of KK modes

1.2 Brane-worlds and M theory

1.3 Heuristics of KK modes

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