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Brane and bulk
The central idea is that the visible, four-dimensional universe is restricted to a brane inside a higher-dimensional space, called the "bulk" (also known as "hyperspace"). If the additional dimensions are compact, then the observed universe contains the extra dimensions, and then no reference to the bulk is appropriate. In the bulk model, at least some of the extra dimensions are extensive (possibly infinite), and other branes may be moving through this bulk. Interactions with the bulk, and possibly with other branes, can influence our brane and thus introduce effects not seen in more standard cosmological models.
Why gravity is weak and the cosmological constant is small
Some versions of brane cosmology, based on the large extra dimension idea, can explain the weakness of gravity relative to the other fundamental forces of nature, thus solving the so-called hierarchy problem. In the brane picture, the other three forces (electromagnetism and the weak and strong nuclear forces) are localized on the brane, but gravity has no such constraint and propagates on the full spacetime, called bulk. Much of the gravitational attractive power "leaks" into the bulk. As a consequence, the force of gravity should appear significantly stronger on small (subatomic or at least sub-millimetre) scales, where less gravitational force has "leaked". Various experiments are currently under way to test this. Extensions of the large extra dimension idea with supersymmetry in the bulk appears to be promising in addressing the so-called cosmological constant problem.
Models of brane cosmology
One of the earliest documented attempts to apply brane cosmology as part of a conceptual theory is dated to 1983.
The authors discussed the possibility that the Universe has (3+N)+1 dimensions, but ordinary particles are confined in a potential well which is narrow along N spatial directions and flat along three others, and proposed a particular five-dimensional model.
In 1998/99 Merab Gogberashvili published on arXiv a number of articles where he showed that if the Universe is considered as a thin shell (a mathematical synonym for "brane") expanding in 5-dimensional space then there is a possibility to obtain one scale for particle theory corresponding to the 5-dimensional cosmological constant and Universe thickness, and thus to solve the hierarchy problem. It was also shown that the four-dimensionality of the Universe is the result of the stability requirement found in mathematics since the extra component of the Einstein field equations giving the confined solution for matter fields coincides with one of the conditions of stability.
In 1999 there were proposed the closely related Randall–Sundrum (RS1 and RS2; see 5 dimensional warped geometry theory for a nontechnical explanation of RS1) scenarios. These particular models of brane cosmology have attracted a considerable amount of attention.
As of now, no experimental or observational evidence of 
- Session D9 - Experimental Tests of Short Range Gravitation.
- Aghababaie, Burgess, Parameswaran, Quevedo (2003-04-29). "Towards a naturally small cosmological constant from branes in 6-D supergravity". Nucl.Phys. B680 (2004) 389-414.
- Burgess, van Nierop (2011-08-01). "Technically Natural Cosmological Constant From Supersymmetric 6D Brane Backreaction". Phys.Dark Univ. 2 (2013) 1-16.
- Burgess, van Nierop, Parameswaran, Salvio, Williams (2012-10-19). "Accidental SUSY: Enhanced Bulk Supersymmetry from Brane Back-reaction". JHEP 1302 (2013) 120.
- V. A. Rubakov and M. E. Shaposhnikov,Do we live inside a domain wall?, Physics Letters B 125 (1983) 136–138.
- M. Gogberashvili, Hierarchy problem in the shell universe model, Arxiv:hep-ph/9812296.
- M. Gogberashvili, Our world as an expanding shell, Arxiv:hep-ph/9812365.
- M. Gogberashvili, Four dimensionality in noncompact Kaluza–Klein model, Arxiv:hep-ph/9904383.
- Musser, George; Minkel, JR (2002-02-11). "A Recycled Universe: Crashing branes and cosmic acceleration may power an infinite cycle in which our universe is but a phase". Scientific American Inc. Retrieved 2008-05-03.
- CMS Collaoration, "Search for Microscopic Black Hole Signatures at the Large Hadron Collider", http://arxiv.org/abs/1012.3375
- Brax, Philippe; van de Bruck, Carsten (2003). "Cosmology and Brane Worlds: A Review". arXiv:hep-th/0303095. – Cosmological consequences of the brane world scenario are reviewed in a pedagogical manner.
- Langlois, David (2002). "Brane cosmology: an introduction". arXiv:hep-th/0209261. – These notes (32 pages) give an introductory review on brane cosmology.
- Papantonopoulos, Eleftherios (2002). "Brane Cosmology". arXiv:hep-th/0202044. – Lectures (24 pages) presented at the First Aegean Summer School on Cosmology, Samos, September 2001.
- Brane cosmology on arxiv.org
- Dimensional Shortcuts - evidence for sterile neutrino; (August 2007; Scientific American)