Randall-Sundrum model

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In theoretical physics, the Randall-Sundrum model is a mathematical approach for the uniform description of the fundamental forces in the universe . It was proposed in 1999 by the physicists Lisa Randall and Raman Sundrum and describes the universe with the introduction of an additional fifth dimension as a curved space-time model , specifically as anti-de-sitter spacetime (abbreviated AdS 5 ). In this space-time there are two four-dimensional branes , one of which corresponds to our visible universe and the other has Planck dimensions , is separated and hidden from the first via the fifth dimension, but interacts gravitationally with the first.

relevance

The Randall-Sundrum model is one of the first models of brane cosmology and was the first to propose an extra dimension that was not on the Planck scale , but extended to macroscopic lengths (finite or infinite). Previously, Kaluza-Klein models were used in string theory , which go back to a theory by Oskar Klein (1926) and Theodor Kaluza , which combined gravity and electrodynamics (the two basic forces known at the time) in a five-dimensional space-time in which the fifth dimension " tiny “ rolled up ( compacted ) dimensions. The principle was expanded and generalized to more dimensions in string theory.

In this way it offers the possibility of solving several fundamental problems in physics:

  • With the help of the Higgs mechanism , it explains why elementary particles have a mass , but gravity - compared to the other interaction forces - is many times weaker.
  • It also describes a consistent model that enables the unification of all previously known basic forces, regardless of string theory and supersymmetry . This was shown by the works of Lisa Randall and Matthew Schwartz as well as Alex Pomarol .

History of origin

The Randall-Sundrum model, referred to by Randall as 5-dimensional warped geometry theory (German: theory of a five-dimensional curved spatial geometry), arose as an attempt to solve the hierarchy problem in the standard model of particle physics . The theory is based on preliminary work by Petr Hořava and Edward Witten for the Hořava-Witten model . Strictly speaking, there are actually two Randall-Sundrum models RS-1 and RS-2, the second being an extension of the first approach.

RS-1 model

As in the Horava-Witten model , in the Randall-Sundrum model 1 the elementary particles known from the standard model are also located in one of two four-dimensional branes that are located at the opposite ends of an extra dimension. It describes our visible universe including three of the basic forces acting in it ( electromagnetic , weak and strong interaction ) and the elementary particles of the standard model on the TeV energy scale. The other bran has the dimension of the Planck scale . They and the empty space ( bulk ) in between are hidden because elementary particles and light cannot get into the space in between. Only the graviton , which transmits gravity as the fourth basic force, can penetrate the bulk and connect matter in both boundary worlds with one another.

In the Randall-Sundrum model 1 the fifth dimension has a finite extent.

RS-2 model

The Randall-Sundrum Model 2 , which was developed later, expands and simplifies the Randall-Sundrum Model 1 in one essential detail, in which it gets by with one instead of two branes. The fifth dimension is unlimited. The probability of the presence of gravitons in the fifth dimension is concentrated on the proximity of our world and also decreases exponentially . The extension of the effect of gravity to an unlimited fifth dimension could explain why gravity is so many orders of magnitude weaker than the other forces of interaction.

Experimental evidence

Since the experimental proof of the effects predicted by string theory is only possible in excessively high energy ranges, the methods known today for particle acceleration would require systems that required dimensions of the order of magnitude of our galaxy . Because of this, string theory was considered unverifiable for many years.

In contrast, the Randall-Sundrum model provides predictions (e.g. the existence of small Kaluza particles ) that can be checked with the Large Hadron Collider at the European Nuclear Research Center CERN near Geneva .

Further development

In the course of the last few years, many other models have been developed, some of which differ significantly from the Randall-Sundrum model in terms of their effects (e.g. on the expansion of the universe ). For example, the empty bulk assumed in the RS model was expanded by models with a scalar field in the bulk, as in the Ekpyrotic scenario and the cyclic universe . Here the branes become dynamic in interaction with the scalar field, can oscillate against one another and even penetrate one another.

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