Warped Passages - Lisa Randall [200]
The Goldberger-Wise paper made it clear that the warped two-brane scenario really was a solution to the hierarchy problem. And the fact that the separation between the branes could be fixed was important for another reason. If the distance between the branes was undetermined, the branes could move closer together or further apart as the temperature and energy of the universe evolves. If the brane separation could change, or if different sides of the five-dimensional universe could expand at different rates, the universe would not evolve in the way it’s supposed to in four dimensions. Since astrophysicists have tested the expansion of the universe late in its evolution, we know that recently the universe has expanded as if it were four-dimensional.
With the Goldberger-Wise stabilization mechanism, the warped five-dimensional universe agrees with cosmological observations. Once the branes are stabilized with respect to each other, the universe would evolve as if it were four-dimensional, even if it actually has five dimensions. Even though there would be a fifth dimension, the stabilization would rigidly constrain different places along the fifth dimension so that they would evolve in the same way, and the universe would behave as it would in four dimensions. Since the Goldberger-Wise stabilization should happen relatively early on, the warped universe would look four-dimensional for most of its evolution.
Once stabilization and cosmology were understood, the warped geometry solution to the hierarchy problem was in business. Many other interesting developments about this warped geometry soon followed. One of these was unification of forces. All forces, including gravity, might be unified at high energies in the warped geometry we’re considering!
Warped Geometry and Unification of Forces
Chapter 13 explained how a major feather in the cap of supersymmetry is that it can successfully accommodate the unification of forces. Extra-dimensional theories that addressed the hierarchy problem seemed to forfeit this potentially important development. Since we have not seen any conclusive experimental evidence for unification, such as proton decay, this is not necessarily a major loss, as we don’t yet know for certain that unification is correct. Nonetheless, three lines meeting at a point is intriguing and might presage something meaningful. Even if unification is not yet firmly established, we shouldn’t abandon it too hastily.
Alex Pomarol, a Spanish physicist now at the University of Barcelona, observed that unification of forces can also occur in warped geometry. However, the setup he considered is slightly different; the electromagnetic, weak, and strong forces are not confined to a brane, but are instead present in the full five-dimensional bulk. The gauge bosons of the Standard Model—the gluons, the Ws, the Z, and the photon—are not stuck on a three-plus-one-dimensional brane.
According to string theory, gauge bosons could be stuck on a higher-dimensional brane or, along with gravity, they too could be in the bulk. Unlike the graviton, which must arise from a closed string, gauge bosons and charged fermions can correspond to either open or closed strings—it depends on the model. And according to whether they arise from open or closed strings, gauge bosons and fermions will be either stuck on a brane or free to move in the bulk.
In the large extra-dimensional scenario, had nongravitational forces been in the bulk, they would have been far too weak to agree with observations. Bulk forces would have spread throughout an enormous bulk space. Therefore, as with gravity, they too would have been extremely diluted. This would be unacceptable because we have measured the forces’ strengths to be much larger than this theory would have predicted.
But if additional dimensions are not large, as is the case in the warped geometry, there is no problem with the nongravitational forces in the five-dimensional bulk. The only thing that