braneworld

The braneworld is a contemporary picture of our Universe, which speculates that our visible Universe may be confined to a three-dimensional volume which resides in a higher-dimensional space. This picture is motivated by superstring theory and M-theory, and if proven right constitutes a major revision of our understanding of the Universe. There is as yet no observational support for the scenario.

The brane and the bulk

The word ‘brane’ is short for membrane, and first appeared in the late 1980s amongst researchers working at the theoretical end of string theory. It had become apparent that as well as one-dimensional strings, it was possible to consider fundamental objects with higher dimensionality. A two-dimensional surface was known as a membrane, but since string theory postulates that there are nine spatial dimensions there is no reason to stop at two dimensions; one can have three, four, five and more dimensional objects residing in this space. Probably initiated as a rather weak pun, the jargon for such objects became p-branes, where p indicates the dimension of the object—superstrings would be 1-branes. Nowadays they are commonly just called branes. In the braneworld scenario, we are particularly interested in 3-branes, being objects with three spatial dimensions just as our Universe appears to have.

In the simplest superstring scenarios, the strings are not allowed to end and so must form loops. However this changes in the presence of a brane; the strings are still not permitted to end in empty space, but they may end on the brane, where their endpoints represent fundamental particles. Because the string ends are not permitted to detach from the brane, the particles are confined to it.

From there it is a short step to the braneworld concept. The particles represented by the string ends are not some mysterious hypothetical particles—they are the particles in the Universe that we are made of. Because they are confined to the brane, our Universe appears to us to have three space dimensions, whereas in reality there are more. The full space, in which the brane is embedded, is known as the bulk. This is schematically illustrated in Fig. 1, for the simplified situation of a two-dimensional Universe embedded in a three-dimensional bulk.

Not all forces are tied to the brane, however. In superstring theories of the kind where strings can end on branes, there are also loops of string which, having no ends, need not stay with the brane but rather can travel freely through the bulk. These string loops are responsible for the gravitational force. Gravity, then, is able to penetrate the bulk, and only under restricted circumstances will behave as if it too were confined to the brane. This offers the best prospect for experimental verification of the braneworld idea.

The Randall–Sundrum braneworld

The full M-theory motivated braneworld picture, sometimes called Horava–Witten theory after its originators Petr Horava and Edward Witten, is an extremely complicated scenario. Within this theory, based on the full eleven-dimensional M-theory, six of the space dimensions are compactified to very small sizes in the same manner as in superstring theory, but the final extra dimension has a different status and may be larger (this is the dimension used to relate eleven-dimensional M-theory to ten-dimensional superstring theory). In order to understand its implications, a lot of work has been done in the context of a much simplified version (what physicists often call a toy model) invented by Lisa Randall and Raman Sundrum in 1999, and called the Randall–Sundrum braneworld.

In the Randall–Sundrum scenario, it is assumed that there is only a single extra dimension, giving a bulk with five space-time dimensions and a brane with three space and one time dimension embedded within it (just as in Fig. 1, with one extra dimension added to each). Then one can consider the distance from the brane into the extra dimension. Randall and Sundrum discovered a remarkable feature. If the brane contains mass (very reasonable since it is full of stuff), then this mass can cause a curvature in the extra dimension; this is just the basic result of Einstein's general relativity theory that the presence of matter curves space giving gravity. In this case, the extra dimension develops a strong curvature, so strong in fact that there is an event horizon which means that even gravitational forces can only act a finite distance away from the brane. This naturally means that even the gravitational force is effectively confined to the brane, as required if the model is to have a chance of matching observations.

Fig. 1. A schematic of the braneworld. Our Universe (here displayed as two-rather than three-dimensional) is confined to a surface known as the ‘brane’. Only the gravitational force sees the full higher-dimensional space known as the ‘bulk’. The gravitational force is mediated by loops of string which travel freely in the bulk. Segments of string have their ends fixed to the brane, the endpoints representing the fundamental particles we see. The brane is infinite in extent along its two dimensions, rather than bounded as it appears in the figure.

Multiple branes

The Randall–Sundrum scenario is elegantly simple, but more complex scenarios exist which contain multiple branes. A common set-up is to have two parallel branes with the bulk wedged between them like a sandwich (see Fig. 2); the full Horava–Witten theory is of this form. In this type of scenario there is no meaning to the region outside the two branes; the entire space-time is the central bulk bounded by a brane at each edge. We would live on one of these boundary branes.

This scenario raises the possibility that interesting things, including other civilizations, might reside on the second brane. If so, they could in principle be extremely near, even just tiny fractions of a metre, but as the separation is in the untraversable extra dimension it is a distance we cannot cross. It would be extremely difficult to detect their presence as only gravitational signals can be sent across the bulk. Either generating or detecting such gravitational waves is well beyond our current technical capability.

An interesting scenario is that the dark matter in the Universe, whose presence has only been detected through its gravitational influence, might reside on a different brane. The formation of galaxies in our Universe may then be due to the clumping of material in an entirely separate Universe. If so, then by definition the gravitational effect of dark matter is all we will ever feel, and direct dark matter detection experiments are doomed to failure.

Fig. 2. A Universe with two branes. The bulk is the slab between the two branes. There is no meaning to the region outside the branes. The branes extend infinitely along their two dimensions.

Large extra dimensions

If extra dimensions can exist, how large can they be? The usual braneworld scenarios presume that they are extremely small indeed, given for instance by the characteristic length scale of fundamental physics, the Planck length, or at least the scale characteristic of grand unification. But there is no reason of principle why they should be so small, and indeed it was proposed in 1998 by Nima Arkani-Hamed, Savas Dimopoulos, and Gia Dvali that their size could be as large as a millimetre. Their reasoning was that the only signature of large extra dimensions is a modification to the gravitational force, and because gravity is so weak no-one knew whether or not Newton's law of gravity was still valid on the millimetre scale. Subsequently delicate experiments have confirmed Newton's theory down to length scales rather smaller than that, but it still remains possible that the extra dimensions are significantly larger than microscopic scales.

Braneworld cosmology

Braneworld cosmology is a subject in its infancy, but one which proposes a substantial rewrite of our view of cosmology, particularly in the early Universe. Amongst the new ingredients the braneworld brings to cosmology are:

• Gravitational forces can penetrate the bulk. At low energies the structure of the theory must prevent this to avoid violation of our everyday experience of gravity, but at very high energies there can be an effect. Indeed, the Randall–Sundrum scenario predicts a high-energy modification to the Friedmann equation describing the expansion of the Universe, which may for instance alter how cosmological inflation takes place.
• The influence of other branes may be important. If a second brane moves relative to ours, that can modify the physics on our own brane. Indeed, Dvali and Henry Tye proposed in 1998 that such inter-brane dynamics might be responsible for inflation.
• Branes might collide, as exploited in the ekpyrotic Universe and cyclic Universe models. Such collisions may correspond to the big bang as experienced by observers on the brane.

All of these topics, and more, are under intense investigation at present.

A final curiosity worth mentioning is that in one viewpoint the expansion of the Universe can be interpreted as due to the motion of our brane through the bulk. One of the first lessons people are taught in cosmology is that the question ‘What is the Universe expanding into?’ has no answer; it is space itself which is expanding. According to the braneworld the question might not have been so stupid after all, and the answer is that the Universe is expanding into an extra dimension.

Bibliography and More Information about braneworld

• Randall, L. Warped Passages: Unravelling the Universe's Hidden Dimensions, Allen Lane, 2005.