hysics is currently in a state of turmoil over the number of dimensions that comprise space-time. This turbulence of theory is not causing any rough rides through laboratory space, but it’s seat-belt time for cosmological excursions. So while condensed matter physicists and other lab-scale practitioners can sleep in peace, the millennial fundamentalists are shaking the very foundations of 20th century theory. This attack on old values is picked up by papers #4 and #5 in the Physics Top Ten.

How many dimensions are there? That’s not easy. Sure, we have three spatial dimensions plus time. And the physics of the four-dimensional framework of space-time is all encapsulated in Einstein’s general theory of relativity, a hugely successful paradigm. But cosmology raises many questions that go beyond the textbook presentation of general relativity. For example, when we run the universe backwards we reach a state of extreme matter and energy density right after the big bang. What theory can we use to describe the universe at the earliest times, when gravity needs folding into quantum theory? And at low energies, when the universe has expanded dramatically due to inflation, how can we account for the puzzles of dark energy and dark matter that weigh in at 97% of the rest mass of the universe?

String theory offers hope of a solution to these cosmological problems, and it may well be the case that cosmology is the only arena in which string theory is testable. Back in the 1980s string theory had so many strands that the theorists were in a complete tangle. There were five 10D supergravity theories and one 11D theory, all of them assuming that the higher spatial dimensions are extremely compact. But this hyperspace knot unraveled in the 1990s: theorists proposed that higher-dimensional extended objects, known as branes, could be embedded in spaces including five or six large dimensions. In two dimensions the brane is a sheet, or membrane ("M-brane") and in three dimensions a real world just like ours. The theoretical revolution is that our 3-brane could be one of many located in a 5D space. What’s compelling about this picture is that the weakness of the gravitational force can be explained away by saying that it leaks into the extra dimensions.

Our two hot papers, #4 and #5, look at a 3-brane world locked into a five-dimensional bulk space-time space. In this picture all the forces except gravity are confined to three dimensions. Pierre Binetruy (University of Paris XI) and his colleagues introduce #4 by pointing out that recent theoretical activity centers on the possibility that our three-dimensional world is embedded in a higher dimensional space. They tackle the cosmology of this situation. In 4D space-time the Friedmann equations describe the evolution of a uniform, homogeneous, and isotropic universe. Our French paper, #4, has become highly cited because it derives the equivalent of the Friedmann equation for a 3-brane in higher dimensional space. This relation depends only on the matter and energy content of the brane. This breakthrough allows theorists to explore the cosmology of brane worlds. The old question, "what is our universe expanding into?" is now answerable: a five-dimensional bulk.

For Science Watch, Binetruy commented: "Our equations take a different form from those derived in general relativity. Much of the work following ours has investigated various aspects of the cosmology, and in particular used our equations to characterize homogeneous cosmology."

Hot Paper #5 was developed at a string theory workfest held at the University of Cambridge, where Isaac Newton developed the first mathematical theory of gravity. While in Cambridge, Tetsuya Shiromizu (University of Tokyo) and his collaborators derived in covariant form the gravitational equations of a 3-brane world in five-dimensional space-time. In the low-energy limit these correspond to the textbook Einstein equations. Coauthor Misao Sasaki (Osaka University) had this comment for Science Watch: "We’ve derived the gravitational equations as seen by an observer on the brane. They look like the Einstein equations but they have two additional terms, which arise from the fifth dimension. One of these terms contains all the information on five-dimensional gravity, and that’s what has excited the interest of the researchers who are citing our work. If this term could be proved experimentally it will give us clear evidence that we are living in a brane-world. Such evidence could come from studies of the fluctuations in the cosmic microwave background, or it may show up in the gravitational waves from collapsing stars or merging binary stars." This paper is clearly of a fundamental kind; the High-Energy Physics electronic database, which includes citations in dozens of as-yet unpublished papers, is registering over 250 hits. The attention that #4 and #5 received this period suggests that brane-world cosmology is in transit from the backwaters to the main stream.