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Unformatted text preview: arXiv:hep-th/0209261v1 30 Sep 2002 1 Brane cosmology: an introduction David Langlois ) GReCO, Institut dAstrophysique de Paris 98 bis, Boulevard Arago, 75014 Paris, France (Received February 1, 2008) These notes give an introductory review on brane cosmology. This subject deals with the cosmological behaviour of a brane-universe, i.e. a three-dimensional space, where ordinary matter is confined, embedded in a higher dimensional spacetime. In the tractable case of a five-dimensional bulk spacetime, the brane (modified) Friedmann equation is discussed in detail, and various other aspects are presented, such as cosmological perturbations, bulk scalar fields and systems with several branes. 1. Introduction It has been recently suggested that there might exist some extra spatial di- mensions, not in the traditional Kaluza-Klein sense where the extra-dimensions are compactified on a small enough radius to evade detection in the form of Kaluza-Klein modes, but in a setting where the extra dimensions could be large, under the as- sumption that ordinary matter is confined onto a three-dimensional subspace, called brane (more precisely 3-brane, referring to the three spatial dimensions) embedded in a larger space, called bulk . Altough the idea in itself is not completely new 1) , the fact that it might be connected to recent string theory developments has suscitated a renewed interest. In this respect, an inspiring input has been the model suggested by Horava and Witten 2) , sometimes dubbed M-theory , which describes the low energy effective theory corresponding to the strong coupling limit of E 8 E 8 heterotic string theory. This model is associated with an eleven-dimensional bulk spacetime with 11-dimensional supergravity, the eleventh dimension being compactified via a Z 2 orbifold symmetry. The two fixed points of the orbifold symmetry define two 10-dimensional spacetime boundaries, or 9-branes, on which the gauge groups are defined. Starting from this configuration, one can distinguish three types of spatial dimensions: the orbifold dimension, three large dimensions corresponding to the ordinary spatial directions and finally six additional dimensions, which can be compactified in the usual Kaluza- Klein way. It turns out that the orbifold dimension might be larger than the six Kaluza-Klein extra dimensions, resulting in an intermediary picture with a five- dimensional spacetime, two boundary 3-branes, one of which could be our universe, and a large extra-dimension. This model provides the motivating framework for many of the brane cosmological models. This concept of a 3-brane has also been used in a purely phenomenological way by Arkani-Hamed, Dimopoulos and Dvali 3) (ADD) as a possible solution to the ) email@example.com 2 David Langlois hierarchy problem in particle physics. Their setup is extremely simple since they consider a flat (4+ n )-dimensional spacetime, thus with n compact extra dimensions with, for simplicity, a torus topology and a common size...
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This note was uploaded on 04/16/2008 for the course PHYS 101 taught by Professor Ballz during the Spring '08 term at IUP.
- Spring '08