1. A Brief Summary of the Modern Particle Physics

There are four fundamental forces in the realm of physics today; gravitation, electromagnetism, the weak force, and the strong force. For most of the twentieth century, physicists have worked vigorously to combine or unify these forces into one, in much the same way Maxwell combined the seemingly disparate forces of electricity and magnetism. Great progress has been made to unify three of the four forces, excluding the realm of gravitation. The first breakthrough came with the unification of electromagnetism and the weak force into the electroweak force ⁽²⁰⁾. This work was done primarily by Glashow, Salam, and Weinberg [39], [40] in the late sixties. Although their theory was not realized until 1971, when the work of 'tHooft showed their theory and all other Yang-Mills theories could be renormalized [38, Chapter 1]. Later work was done to unify the strong and electroweak under the symmetry ⁽²¹⁾

This model is referred to as the Standard Model and has made a number of predictions, which have been verified by experiment. However, there are many aspects of the model that suggest it is incomplete. The model produces accurate predictions for such phenomena as particle scattering and absorption spectra. Although, the model requires the input of some 19 parameters. These parameters consist of such properties as particle masses and charge. But one would hope for a model that could explain most, if not all of these parameters. This can be accomplished by taking the symmetry group of the standard model and embedding it in a higher group with one coupling. This coupling, once the symmetry is broken, would result in the parameters of the standard model. Theories of this type are often referred to as grand unified theories (GUTs). Many such models have been proposed along with some very different approaches. Some current efforts go by the interesting names; Superstring theory, Supersymmetry, Technicolor, SU(5), etc.

Of all the proposed theories the most promising at the current moment is Superstring theory. In addition to unifying the three forces, this theory can also include the fourth force, gravity. These theories (there's more than one) can be summarized quite simply. In the standard model, and in all undergraduate physics courses, particles are considered points. If you have ever given any thought to this, it mostly likely has troubled you. You are not alone and the creators of string theory had this very idea as their motivation. String theory assumes that particles are not points, instead they are tiny vibrating strings. The modes of vibration of the string give rise to the particle masses, charges, etc. This simple picture, along with the idea of supersymmetry, produces a model that presents the standard model as a low energy approximation.

Supersymmetric theories differ from the standard model, by the existence of a supersymmetric partner for each particle in the standard model. For example, for each half-integer spin lepton there corresponds an integer spin slepton (thus, it is a boson). These supersymmetric partners are not observed today, because they are extremely unstable at low temperatures. However, some versions of the theory suggest a conservation of supersymmetric number. If this is the case, then all of the supersymmetric particles would be expected to decay into a lowest energy mode referred to as the neutralino. As a result, this particle is one of the leading candidates for cold dark matter [9, Chapter 6].

The link with cosmology is further exhibited because the hot Big Bang model predicts that at some time in the past, the temperature was high enough for GUTs to be tested. Because it is impossible to recreate these temperatures today, the universe offers the only experimental apparatus to examine the physics of these unified theories ⁽²²⁾ As the universe expands, and thus cools (T ~ a^-1), the supersymmetry is broken and the particles manifest themselves as the different particles that we observe today.

Superstring theorists have attempted to unify these supersymmetric models with gravity into a so-called Theory Of Everything (TOE). Some theories have relaxed the supersymmetric requirement and still produce TOEs by the addition of higher dimensions. Some proposed TOEs worth mentioning are: Superstrings, M-Theory, Supergravity (SUGRA), and Twistor Gravity. The details of these theories need not concern the reader at this point ⁽²³⁾

The common aspect of all of these theories is that they are usually associated with some sort of symmetry breaking mechanism, which in turn gives rise to a phase transition. In the past, cosmologists assumed that these effects would be negligible. Guth showed these effects can't be ignored. If they are, they predict a world dominated by massive magnetic monopoles (in the case of SU(5)). One may argue that SU(5) is not known to be the correct theory. This is true. However, most physicists believe that any correct unified theory will exhibit symmetry breaking. Moreover, the electroweak theory has been verified experimentally and exhibits a symmetry breaking that could have given rise to inflation.

²⁰ As an aside to the interested reader, the electroweak force is not really a unified force, in the strict sense of the world, because the theory contains two couplings. See [38] for more. Back.
²¹ See [41] for a description of symmetries and how they relate to particle physics. Back.
²² This statement is not truly accurate. Particle theories, such as GUTs, will be further verified with the detection of the symmetry breaking, or Higgs particle. This particle should be detectable around 1Tev, which is currently possible. Back.
²³ The reader is again referred to the electronic preprints at Los Alamos for the latest information on Superstring theory and the like: http://xxx.lanl.gov. Back.