Editing Hierarchy problem (section)

==== Braneworld models ====
{{Main article|Brane cosmology}}

In 1998 [[Nima Arkani-Hamed]], [[Savas Dimopoulos]], and [[Gia Dvali]] proposed the '''ADD model''', also known as the model with [[large extra dimensions]], an alternative scenario to explain the weakness of [[gravity]] relative to the other forces.<ref name="ADD1">{{cite journal |last1=Arkani-Hamed |first1=N. |last2=Dimopoulos |first2=S. |last3=Dvali |first3=G. |year=1998 |title=The Hierarchy problem and new dimensions at a millimeter |journal=[[Physics Letters]] |volume=B429 |issue=3–4 |pages=263–272 |arxiv=hep-ph/9803315 |bibcode=1998PhLB..429..263A |doi=10.1016/S0370-2693(98)00466-3 |s2cid=15903444}}</ref><ref name="ADD2">{{cite journal |last1=Arkani-Hamed |first1=N. |last2=Dimopoulos |first2=S. |last3=Dvali |first3=G. |year=1999 |title=Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity |journal=[[Physical Review]] |volume=D59 |issue=8 |page=086004 |arxiv=hep-ph/9807344 |bibcode=1999PhRvD..59h6004A |doi=10.1103/PhysRevD.59.086004 |s2cid=18385871}}</ref> This theory requires that the fields of the [[Standard Model]] are confined to a four-dimensional [[membrane (M-Theory)|membrane]], while gravity propagates in several additional spatial dimensions that are large compared to the [[Planck scale]].<ref>For a pedagogical introduction, see {{cite conference |last=Shifman |first=M. |author-link=Mikhail Shifman |year=2009 |title=Large Extra Dimensions: Becoming acquainted with an alternative paradigm |journal=International Journal of Modern Physics A |volume=25 |issue=2n03 |pages=199–225 |conference=Crossing the boundaries: Gauge dynamics at strong coupling |location=Singapore |publisher=World Scientific |arxiv=0907.3074 |bibcode=2010IJMPA..25..199S |doi=10.1142/S0217751X10048548}}</ref>

In 1998–99 [[Merab Gogberashvili]] published on [[arXiv]] (and subsequently in peer-reviewed journals) 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 it is possible to obtain one scale for particle theory corresponding to the 5-dimensional [[cosmological constant]] and Universe thickness, and thus to solve the hierarchy problem.<ref>{{cite journal |last1=Gogberashvili |first1=Merab |last2=Ahluwalia |first2=D. V. |year=2002 |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 |bibcode=2002IJMPD..11.1635G |doi=10.1142/S0218271802002992 |s2cid=119339225}}</ref><ref>{{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}}</ref><ref>{{cite journal |last=Gogberashvili |first=Merab |year=1999 |title=Four Dimensionality in Non-Compact 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}}</ref> It was also shown that four-dimensionality of the Universe is the result of a [[Stability theory|stability]] requirement since the extra component of the [[Einstein field equations]] giving the localized solution for [[matter]] fields coincides with one of the conditions of stability.

Subsequently, there were proposed the closely related [[Randall–Sundrum model|Randall–Sundrum]] scenarios which offered their solution to the hierarchy problem.