Brane cosmology

The central idea is that the visible, three-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 dimension, 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.

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 hierarchy problem. In the brane picture, the electromagnetic, weak and strong nuclear force are localized on the brane, but gravity has no such constraint and propagates on the full spacetime, called the 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.[1] Extensions of the large extra dimension idea with supersymmetry in the bulk appears to be promising in addressing the so-called cosmological constant problem.[2][3][4]

One of the earliest documented attempts to apply brane cosmology as part of a conceptual theory is dated to 1983.[5]

The authors discussed the possibility that the Universe has ${\displaystyle (3+N)+1}$ dimensions, but ordinary particles are confined in a potential well which is narrow along ${\displaystyle N}$ 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.[6][7] Gogberashvili also showed 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.[8]

In 1999, there were proposed the closely related Randall–Sundrum scenarios, RS1 and RS2. (See Randall–Sundrum model for a nontechnical explanation of RS1). These particular models of brane cosmology have attracted a considerable amount of attention. For instance, the related Chung-Freese model, which has applications for spacetime metric engineering, followed in 2000.[9]

Later, the ekpyrotic and cyclic proposals appeared. The ekpyrotic theory hypothesizes that the origin of the observable universe occurred when two parallel branes collided.[10]

As of now, no experimental or observational evidence of large extra dimensions, as required by the Randall–Sundrum models, has been reported. An analysis of results from the Large Hadron Collider in December 2010 severely constrains the black holes produced in theories with large extra dimensions.[11] The recent multi-messenger gravitational wave event GW170817 has also been used to put weak limits on large extra dimensions.[12][13]

• Kaluza–Klein theory
• Loop quantum cosmology

• Brane cosmology on arxiv.org
• Brax, Philippe; van de Bruck, Carsten (2003). "Cosmology and Brane Worlds: A Review". Classical and Quantum Gravity. 20 (9): R201–R232. arXiv:hep-th/0303095. Bibcode:2003CQGra..20R.201B. doi:10.1088/0264-9381/20/9/202. S2CID 9623407. – Cosmological consequences of the brane world scenario are reviewed in a pedagogical manner.
• Dimensional Shortcuts - evidence for sterile neutrino; (August 2007; Scientific American)
• Langlois, David (2003). "Brane cosmology: an introduction". Progress of Theoretical Physics Supplement. 148: 181–212. arXiv:hep-th/0209261. Bibcode:2002PThPS.148..181L. doi:10.1143/PTPS.148.181. S2CID 9751130. – These notes (32 pages) give an introductory review on brane cosmology.
• Papantonopoulos, Eleftherios (2002). "Brane Cosmology". Cosmological Crossroads. Lecture Notes in Physics. Vol. 592. pp. 458–477. arXiv:hep-th/0202044. Bibcode:2002LNP...592..458P. doi:10.1007/3-540-48025-0_15. ISBN 978-3-540-43778-9. S2CID 3084654. – Lectures (24 pages) presented at the First Aegean Summer School on Cosmology, Samos, September 2001.