6.2. Cosmology in the Lab
As we mentioned earlier, unlike any other proposed mechanism for the generation of observable cosmological features, topological defects can be reproduced in the laboratory! In fact, when all relevant lengths are uniformly scaled down, experimentalists have within reach a manageable laboratory experiment that offers a physical equivalent of the early universe. Some years ago, Zurek  proposed testing the Kibble mechanism using the transition that the liquefied noble gas helium-4 makes from its normal state to the superfluid state, which exists at temperatures lower than about 2 degrees above absolute zero and in which fluid flow occurs without any friction.
If liquid helium were rapidly pressure-quenched around the critical temperature, Zurek argued, the rotation of the fluid as a whole would become trapped in a number of isolated vortices - tiny tornadoes, in effect. The vortices, carrying rotation in quantized amounts, would represent defects closely analogous to cosmic strings, and studying their formation might offer interesting hints for cosmology. Of course, although defects in condensed matter systems are topologically identical to those in field theory, there are also some important differences. The dynamics of the laboratory system is nonrelativistic, and friction is the controlling force, whereas in the cosmological case defects can move at almost the speed of light, and gravity is important. An additional technical difficulty is that the infinite and homogeneous nature of the universe before a phase transition cannot be matched by a laboratory sample of finite size.
Dealing with the superfluid transition of helium turned out to be hard, requiring extreme laboratory conditions. Some groups have demonstrated vortex generation, but it remains unclear how well the experimental findings match the Kibble-Zurek predictions. However, a more tractable laboratory analogue has been found, in the form of organic compounds called liquid crystals. In the second half of the 19th century chemists found several materials that behaved strangely around their melting point. In 1850, W. Heintz reported on the peculiarities of stearin, an organic compound used to waterproof paper and make metal polishes and soap. Heated from about 52 to 62 degrees Celsius, stearin first changed from a solid to a cloudy liquid, then took on an opaque coloring, then finally became a clear liquid. Similar behavior was later observed in other biological materials, leading eventually to the recognition of liquid crystals as a new form of matter - which got their badge of honor with the award of the 1991 Nobel Prize in Physics to Pierre-Gilles de Gennes for his accomplishments on order phenomena in liquid-crystal systems.
Liquid crystals are organic compounds with phases intermediate to the liquid and solid phases: They can flow like liquids while retaining anisotropic properties of crystalline solids, meaning that their molecular structure has a spatial alignment or orientation. They can be imagined as crystals whose molecules are able to move around, as in a liquid, while maintaining their relative orientation. For example, nematic liquid crystals consist of rodlike molecules, about 20 angstroms long, which tend to maintain themselves in a parallel alignment. Their structure endows them with useful optical properties. Such materials are used in digital displays, where electrical signals flip the orientation of the crystals, switching them between opaque and reflective states.
Liquid-crystal transitions occur at temperatures ranging from 10 to 200 degrees Celsius and generate structures easily detectable with the naked eye or with a microscope. These transitions proceed by the formation of domains, as different regions within a crystal settle into different alignments, so once again there is the possibility of defect formation. Experiments have shown that networks of defects in nematic crystals evolve in a self-similar manner, meaning that although the characteristic scale of the pattern changes, its maintains the same overall appearance. As we saw in previous sections, such behavior is needed in a cosmological context for strings to be harmless cosmologically and, moreover, eventually useful as progenitors of structure: self-similarity means that the defects contribute a constant fraction of the universe's total energy density from small to large length scales.
Figure 1.21. Cosmological-defect formation can be simulated in the laboratory by observing the transformation of liquid crystal between phases with different optical properties. In this sequence, bubbles of a new phase nucleate in an initially uniform liquid. As the bubbles grow and coalesce, their boundaries develop into structures analogous to cosmic strings. The scale of the pattern grows similarly to the way the scale of a network of cosmic strings increases with cosmic expansion. (Images courtesy of Ajit Srivastava, Institute of Physics, Bhubaneswar, India.)
Recently many groups have succeeded in carrying out a variation of Zurek's original idea using the superfluid transition in another isotope, helium-3, at temperatures close to 1 millikelvin, rather than the higher-temperature transition in helium-4 [see, e.g., Bunkov & Godfrin, 2000] (23). In 1996, Ruutu and collaborators in Helsinki succeeded in heating up a volume of superfluid helium-3 with thermal neutrons to just above the transition temperature, then cooling it back through the superfluid transition. They observed copious production of quantized vortices. The precision in these experiments is such that the number of vortex lines can be monitored, allowing quantitative testing of defect-formation theories. Laboratory tests using both liquid crystals and helium have provided a kind of experimental confirmation of cosmological topological defect theory, increasing the credibility of these ideas.
23 See for instance the internet sites
and http://boojum.hut.fi/research/applied/rotating3he.html Back.