Randall–Sundrum model

In physics, Randall–Sundrum models (also called 5-dimensional warped geometry theory) are models that describe the world in terms of a warped-geometry higher-dimensional universe, or more concretely as a 5-dimensional anti-de Sitter space where the elementary particles (except the graviton) are localized on a (3 + 1)-dimensional brane or branes. In physics, Randall–Sundrum models (also called 5-dimensional warped geometry theory) are models that describe the world in terms of a warped-geometry higher-dimensional universe, or more concretely as a 5-dimensional anti-de Sitter space where the elementary particles (except the graviton) are localized on a (3 + 1)-dimensional brane or branes. The two models were proposed in two articles in 1999 by Lisa Randall and Raman Sundrum because they were dissatisfied with the universal extra-dimensional models then in vogue. Such models require two fine tunings; one for the value of the bulk cosmological constant and the other for the brane tensions. Later, while studying RS models in the context of the anti-de Sitter / conformal field theory (AdS/CFT) correspondence, they showed how it can be dual to technicolor models. The first of the two models, called RS1, has a finite size for the extra dimension with two branes, one at each end. The second, RS2, is similar to the first, but one brane has been placed infinitely far away, so that there is only one brane left in the model. The model is a braneworld theory developed while trying to solve the hierarchy problem of the Standard Model. It involves a finite five-dimensional bulk that is extremely warped and contains two branes: the Planckbrane (where gravity is a relatively strong force; also called 'Gravitybrane') and the Tevbrane (our home with the Standard Model particles; also called 'Weakbrane'). In this model, the two branes are separated in the not-necessarily large fifth dimension by approximately 16 units (the units based on the brane and bulk energies). The Planckbrane has positive brane energy, and the Tevbrane has negative brane energy. These energies are the cause of the extremely warped spacetime. In this warped spacetime that is only warped along the fifth dimension, the graviton's probability function is extremely high at the Planckbrane, but it drops exponentially as it moves closer towards the Tevbrane. In this, gravity would be much weaker on the Tevbrane than on the Planckbrane. Also in this model, any object moving from the Planckbrane to the Tevbrane in the bulk would be growing, becoming lighter, and moving more slowly through time. Distance and time expand near the Tevbrane, and mass and energy shrink near it. This creates an alternate explanation of gravity's weakness in the Tevbrane: everything is lighter. An interesting part of this is that the hierarchy problem is automatically solved. The main scale on the Planckbrane would be the Planck scale. However, the change by 16 units causes the scales to change by 16 orders of magnitude. On the Planckbrane, strings would be 10−33 cm in size, but on the Tevbrane they'd be 10−17 cm. In fact, this makes the mass scale for the Weakbrane based on about a TeV. Therefore, you no longer have the strange range of masses and energies. If this was the case, we should have seen evidence when the Large Hadron Collider began working. The RS1 model attempts to address the hierarchy problem. The warping of the extra dimension is analogous to the warping of spacetime in the vicinity of a massive object, such as a black hole. This warping, or red-shifting, generates a large ratio of energy scales, so that the natural energy scale at one end of the extra dimension is much larger than at the other end: where k is some constant, and η has '−+++' metric signature. This space has boundaries at y = 1/k and y = 1/(Wk), with 0 ≤ 1 / k ≤ 1 / ( W k ) {displaystyle 0leq 1/kleq 1/(Wk)} , where k is around the Planck scale, W is the warp factor, and Wk is around a TeV. The boundary at y = 1/k is called the Planck brane, and the boundary at y = 1/(Wk) is called the TeV brane. The particles of the standard model reside on the TeV brane. The distance between both branes is only −ln(W)/k, though. In another coordinate system,