COSMOLOGY, COSMIC STRINGS NEIL TUROK One of the most active areas of current research in physics and astronomy is the search for a theory of the formation of structure in the universe. Historically, this is a result of the success of two different theories and the attempt to combine them. In astronomy, the Hot Big Bang model of the universe has three big successes. It successfully explains the expansion of the universe, the relic microwave background radiation, and the abundances of the light elements today. The weakness of the standard Hot Big Bang model is that it says nothing about how structure in the universe (galaxies and cluster of galaxies) could have originated. In high-energy physics, the idea that the underlying theory of particles and their interactions has a high degree of symmetry which is broken at low energies forms the basis of the Weinberg-Salam model of the electroweak interactions. Over the last decade many predictions of this model have been confirmed, the discovery of the W and Z particles being the most dramatic. Based on the idea of symmetry breaking, theories which unify all the forces except gravity (grand unified theories), and theories including gravity (superstring theories) have been developed. Unfortunately, at present there are many different theories, and few ways of testing them. One idea, which emerged from particle physics in the early 1980s, was that the same process which broke the symmetry between the particles and forces might break the spatial symmetry of the universe, producing the structure we see today. This is physically a very reasonable idea. In fact, similar processes happen in everyday substances. Most liquids are quite homogeneous and isotropic, which is not surprising, because there is nothing in the description of atoms and their interactions that singles out a particular direction or place in space as different from any other. Cool the liquid, however, and it freezes. The crystal structure of the solid picks a particular direction; but in different regions different directions are chosen. The result is that (unless the process happens very slowly) the solid is formed full of defects where there is a mismatch between neighboring crystalline regions. Cosmic strings are very similar to these defects. They are predicted to occur by some grand unified theories and superstring theories. In the very early universe, at high temperature the fields in these theories are random, just as the atoms of a liquid. The density is quite uniform. As the universe cools below a certain temperature, some of the fields "freeze." As they do so, defects are formed, just as in solids. In different theories, the defects may be at points, along lines, or in sheets. Cosmic strings are the linelike defects: They have special properties which make them well suited to forming structure later in the universe. For topological reasons they cannot have ends; they must form closed loops or continue on forever. The only way to change the length of a string is if it crosses itself and reconnects the other way (Fig. 1), chopping off a loop. This means that if one starts with some strings which wander right across the universe, there is no way to get rid of them completely. At best one can progressively chop more and more of the long string off into loops, and the loops can then radiate away (see Fig. 1). Thus some of the strings formed at very early times (around ******* after the Big Bang in most models predicting strings) survive right up to today. Cosmic strings are very thin: approximately 10*** the radius of a proton! But they are also very massive. 1 meter of cosmic string weighs approximately ***** kg. This is not quite enough for them to form black holes: The dimensionless number measuring their coupling to gravity is *****. Here G is Newton's constant, ** is the mass per unit length of the string and c the speed of light. This would have to be of order unity for the strings to form black holes. Typically, in grand unified theories predicting cosmic strings, one finds *********. When cosmic strings form, some of the string is in the form of closed loops. Most, however, is in the form of very long strings, which wander right across the universe. They are infinite if the universe is infinite, or wrap right around the universe and close back on themselves if it is finite. The universe is filled with a random, tangled network of strings. The motion of the string is quite complicated. However, a remarkable feature of it is that it does not depend at all on the mass per unit length of the string. The tension of the string equals its mass per unit length times ***, so waves propagate on the string at the speed of light. This makes the cosmic string theory very predictive: The distribution of the strings is fully specified at any time. As the universe expands, the long strings chop themselves up into loops. This is a complicated process, but is well described by a simple scaling theory. According to this theory, at any time after the network is produced it has a characteristic scale, and the long strings look like random walks with this scale. The long strings continually chop off a distribution of loops, characterized by this scale. Furthermore, this scale grows linearly with time. The result is that the total density in a long string remains a fixed fraction (approximately ****) of the total density in the universe from the time when strings form right up to the time when density fluctuations start to grow around them, at around **** s. Computer simulations such as those shown in Fig. 2 have confirmed the scaling theory, and have led to predictions of the distribution of the strings as the universe evolves. Sharpening these predictions is a difficult task: The biggest computers can only evolve a network for a factor 100 or so in time, and one must evolve them from ***** s to the time when matter starts clustering around them, about **** s, in order to compare to observations. So developing an analytic understanding of the evolution of the network is an important area of current research. In the simplest picture of how structure forms around the strings, one simply associates one loop of string with one object. A loop 10 pc long has a mass of *** solar masses, and accretes a galaxy mass by today (remember the growth factor of *** mentioned earlier). Likewise a loop of 10 kpc accretes **** solar masses, the mass of a cluster of galaxies. Of course, as it clusters matter around it, it also clusters the loops accreting galaxies. Whilst the mass of the accreted objects depends on *, the pattern in which the galaxies and clusters are laid down does not (this is only true on large scales, where nonlinear effects are not important). Thus the accretion pattern produced by the strings is a clear prediction with no adjustable parameters. Remarkably, the pattern formed by cosmic string loops closely matches the observed pattern of giant galaxy clusters on the sky. Unfortunately, there are still large uncertainties as to whether the loop distribution measured in string simulations is the correct scaling distribution. More detailed calculations of large-scale structure produced by cosmic strings are only just beginning: There are hints that the "wakes" produced by long strings do produce galaxy "sheets," "bubbles," and "filaments," just as the observations indicate. The most exciting aspect of the theory is that there are other completely independent ways of observing the effects of cosmic strings. The most direct way is in the pattern of anisotropy produced in the observed microwave background radiation. If a light ray passes behind a moving string on its path to us, it is shifted towards the blue relative to a ray passing in front of the string. This is a sort of "gravitational slingshot" effect. The result is that if cosmic strings exist, and observations of the microwave background radiation become sensitive to 1 part in 10**(which they are close to doing), one should see stripes in the temperature pattern on the sky! This signal is quite unambiguous and would leave little doubt that cosmic strings actually exist. The second direct effect is gravitational lensing. Light is bent as it passes on either side of a string (Fig. 3). Consequently, a galaxy observed behind a string would be seen as a double image. There are several "lensed" galaxies that have been seen so far, but there is no firm evidence that a cosmic string is responsible: A massive galaxy or dust cloud can produce the same effect. The third test is the gravity wave background. The loops chopped off of the network radiate away into gravity waves: This process is actually crucial to the consistency of the theory because otherwise the small loops would build up and eventually come to dominate the density of the universe. The gravity wave background produced by the radiation from loops has been calculated, and amounts today to 1 part in 1000 of the density of the microwave background density. Amazngly, there are stringent limits on even this low a density in gravity waves. They come from accurate timing measurements on a millisecond pulsar. Basically, t a gravity wave passing through us would move us relative to the pulsar, and cause the frequency of the signals from the pulsar to be Doppler shifted. A random background of gravity waves would therefore lead to "noise" in the pulsar timing data. After various corrections for the evolution of the pulsar, which are believed to be well understood, no such effect is observed. The present status is that the simplest cosmic string theory, explained earlier, is very close to being ruled out by these measurements. Cosmic strings do not have to be so simple. It has also been found that in some simple grand unified theories the cosmic strings are actually superconducting-they can carry enormous electric currents (*******) with zero resistance. This leads to a number of fascinating possibilities. Electric currents can build up on such strings via a "dynamo" effect, and the strings then build up a large magnetic field around them. This leads to a number of new ways for observing strings directly, and to a variety of novel astrophysical phenomena. There are There are other equally speculative theories of the origin of large-scale structure in the universe. The virtue of the simplest cosmic string theory is that it makes quite clear testable predictions. If it is wrong, we shall know soon. Additional Reading Albrecht, A., Brandenberger, R., and Turok, N.(1987). Cosmic strings and cosmic structure. New Scientist 114 (No.1556)40. Albrecht, A. and Turok, N.(1989). Evolution of cosmic string networks. Phys. Rev. D 40 973. Kibble, T.W.B.(1976). Topology of cosmic domains. J. Phys. A 9 1387. Vilenkin, A.(1985). Cosmic strings and domain walls. Phys. Rep. 121 263. Turok, N.(1989). Phase transitions as the origin of large scale structures in the universe. In Particle Physics and Astrophysics: Current Viewpoints, H. Mitter and F. Widder, eds. SpringVerlag, Berlin. See also Cosmology, Clustering and Superclustering; Cosmology, Inflationary Universe; Gravitational Lenses; Gravitational Radiation.