Brane cosmology#Brane and bulk

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The central idea is that the visible, four-dimensional spacetime 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". In 2004, various experiments were under way to test this.{{Cite web |title=Session D9 - Experimental Tests of Short Range Gravitation. |url=https://flux.aps.org/meetings/YR04/APR04/baps/abs/S690.html |website=flux.aps.org}} Extensions of the large extra dimension idea with supersymmetry in the bulk appear to be promising in addressing the so-called cosmological constant problem.{{Cite journal |last1=Aghababaie |first1=Y. |last2=Burgess |first2=C. P. |last3=Parameswaran |first3=S. L. |last4=Quevedo |first4=F. |date=March 2004 |title=Towards a naturally small cosmological constant from branes in 6-D supergravity |journal=Nucl. Phys. B |volume=680 |issue=1–3 |pages=389–414 |arxiv=hep-th/0304256 |bibcode=2004NuPhB.680..389A |doi=10.1016/j.nuclphysb.2003.12.015 |s2cid=14612396}}{{Cite journal |last1=Burgess |first1=C. P. |last2=van Nierop |first2=Leo |date=March 2013 |title=Technically Natural Cosmological Constant From Supersymmetric 6D Brane Backreaction |journal=Phys. Dark Univ. |volume=2 |issue=1 |pages=1–16 |arxiv=1108.0345 |bibcode=2013PDU.....2....1B |doi=10.1016/j.dark.2012.10.001 |s2cid=92984489}}{{Cite journal |last1=P. Burgess |first1=C. |last2=van Nierop |first2=L. |last3=Parameswaran |first3=S. |last4=Salvio |first4=A. |last5=Williams |first5=M. |date=February 2013 |title=Accidental SUSY: Enhanced Bulk Supersymmetry from Brane Back-reaction |url=http://inspirehep.net/record/1191922 |journal=JHEP |volume=2013 |issue=2 |page=120 |arxiv=1210.5405 |bibcode=2013JHEP...02..120B |doi=10.1007/JHEP02(2013)120 |s2cid=53667729}}

One of the earliest documented attempts to apply brane cosmology as part of a conceptual theory is dated to 1983.{{Cite journal |last1=Rubakov |first1=V. A. |last2=Shaposhnikov |first2=M. E. |year=1983 |title=Do we live inside a domain wall? |journal=Physics Letters |series=B |volume=125 |issue=2–3 |pages=136–138 |bibcode=1983PhLB..125..136R |doi=10.1016/0370-2693(83)91253-4}}

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 a number of articles on arXiv where he showed that if we consider the universe as a thin shell (mathematical synonym for "brane") expanding in 5-dimensional space then there is a possibility of obtaining a single scale for particle theory corresponding to the 5-dimensional cosmological constant and the thickness of the universe, thus solving the hierarchy problem.{{Cite journal |last=Gogberashvili |first=M. |date=1998 |title=Hierarchy problem in the shell universe model |journal=International Journal of Modern Physics D |volume=11 |issue=10 |pages=1635–1638 |arxiv=hep-ph/9812296 |doi=10.1142/S0218271802002992 |s2cid=119339225}}{{Cite journal |last=Gogberashvili |first=M. |year=2000 |title=Our world as an expanding shell |journal=Europhysics Letters |volume=49 |issue=3 |pages=396–399 |arxiv=hep-ph/9812365 |bibcode=2000EL.....49..396G |doi=10.1209/epl/i2000-00162-1 |s2cid=38476733}} 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.{{Cite journal |last=Gogberashvili |first=M. |date=1999 |title=Four dimensionality in noncompact Kaluza–Klein model |journal=Modern Physics Letters A |volume=14 |issue=29 |pages=2025–2031 |arxiv=hep-ph/9904383 |bibcode=1999MPLA...14.2025G |doi=10.1142/S021773239900208X |s2cid=16923959}}

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.{{Cite journal |last1=Chung |first1=Daniel J. H. |last2=Freese |first2=Katherine |date=2000-08-25 |title=Can geodesics in extra dimensions solve the cosmological horizon problem? |journal=Physical Review D |volume=62 |issue=6 |pages=063513 |arxiv=hep-ph/9910235 |bibcode=2000PhRvD..62f3513C |doi=10.1103/physrevd.62.063513 |issn=0556-2821 |s2cid=119511533}}

Later, the ekpyrotic and cyclic proposals appeared. The ekpyrotic theory hypothesizes that the origin of the observable universe occurred when two parallel branes collided.{{Cite news |last1=Musser |first1=George |last2=Minkel |first2=J. R. |date=2002-02-11 |title=A Recycled Universe: Crashing branes and cosmic acceleration may power an infinite cycle in which our universe is but a phase |url=http://www.sciam.com/article.cfm?id=a-recycled-universe |access-date=2008-05-03 |publisher=Scientific American Inc.}}

{{see also|Large extra dimension#Empirical tests}}

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.{{Cite journal |year=2011 |title=Search for Microscopic Black Hole Signatures at the Large Hadron Collider |journal=Physics Letters B |volume=697 |issue=5 |pages=434–453 |arxiv=1012.3375 |bibcode=2011PhLB..697..434C |doi=10.1016/j.physletb.2011.02.032 |s2cid=118488193|last1=Khachatryan |first1=V. |last2=Sirunyan |first2=A.M. |last3=Tumasyan |first3=A. |last4=Adam |first4=W. |last5=Bergauer |first5=T. |last6=Dragicevic |first6=M. |last7=Erö |first7=J. |last8=Fabjan |first8=C. |last9=Friedl |first9=M. |last10=Frühwirth |first10=R. |last11=Ghete |first11=V.M. |last12=Hammer |first12=J. |last13=Hänsel |first13=S. |last14=Hartl |first14=C. |last15=Hoch |first15=M. |last16=Hörmann |first16=N. |last17=Hrubec |first17=J. |last18=Jeitler |first18=M. |last19=Kasieczka |first19=G. |last20=Kiesenhofer |first20=W. |last21=Krammer |first21=M. |last22=Liko |first22=D. |last23=Mikulec |first23=I. |last24=Pernicka |first24=M. |last25=Rohringer |first25=H. |last26=Schöfbeck |first26=R. |last27=Strauss |first27=J. |last28=Taurok |first28=A. |last29=Teischinger |first29=F. |last30=Waltenberger |first30=W. |display-authors=1 }} The recent multi-messenger gravitational wave event GW170817 has also been used to put weak limits on large extra dimensions.{{Cite journal |last1=Visinelli |first1=Luca |last2=Bolis |first2=Nadia |last3=Vagnozzi |first3=Sunny |date=March 2018 |title=Brane-world extra dimensions in light of GW170817 |journal=Phys. Rev. D |volume=97 |issue=6 |pages=064039 |arxiv=1711.06628 |bibcode=2018PhRvD..97f4039V |doi=10.1103/PhysRevD.97.064039 |s2cid=88504420}}{{Cite news |last=Freeland |first=Emily |date=2018-09-21 |title=Hunting for extra dimensions with gravitational waves |publisher=The Oskar Klein Centre for Cosmoparticle Physics blog |url=https://ssl.fysik.su.se/okc/internal/blog/hunting-for-extra-dimensions-with-gravitational-waves/ |access-date=2018-11-30 |archive-date=2021-01-27 |archive-url=https://web.archive.org/web/20210127215024/https://ssl.fysik.su.se/okc/internal/blog/hunting-for-extra-dimensions-with-gravitational-waves/ |url-status=dead }}

• Kaluza–Klein theory
• Loop quantum cosmology

• [http://xstructure.inr.ac.ru/x-bin/theme3.py?level=2&index1=-197206 Brane cosmology on arxiv.org].
• {{Cite journal |last1=Brax |first1=Philippe |author-link=Philippe Brax |last2=van de Bruck, Carsten |author-link2=Carsten van de Bruck |year=2003 |title=Cosmology and Brane Worlds: A Review |journal=Classical and Quantum Gravity |volume=20 |issue=9 |pages=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.
• [https://web.archive.org/web/20130124185355/http://www.sciamdigital.com/index.cfm?fa=Products.ViewIssuePreview&ARTICLEID_CHAR=9D2C5D4D-2B35-221B-6C9DB167634A6DDB Dimensional Shortcuts – evidence for sterile neutrino; (August 2007; Scientific American)]
• {{Cite journal |last=Langlois |first=David |author-link=David Langlois |year=2003 |title=Brane cosmology: an introduction |journal=Progress of Theoretical Physics Supplement |volume=148 |pages=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.
• {{Cite book |last=Papantonopoulos |first=Eleftherios |title=Cosmological Crossroads |year=2002 |isbn=978-3-540-43778-9 |series=Lecture Notes in Physics |volume=592 |pages=458–477 |chapter=Brane Cosmology |bibcode=2002LNP...592..458P |doi=10.1007/3-540-48025-0_15 |author-link=Eleftherios Papantonopoulos |s2cid=3084654 |arxiv=hep-th/0202044}} – Lectures (24 pages) presented at the First Aegean Summer School on Cosmology, Samos, September 2001.

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