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Fat branes and the graviton propagator
The weakness of the gravitational force has been successfully explained by postulating the existence of extra dimensions [54,55]. The effect of the extra dimensions is a high-energy modification of Newton's Law of gravity due to the tower of Kaluza-Klein modes. When the extra dimensions are of infinite volume, light Kaluza-Klein modes may dominate even at low energies [56,57,58]. Thus, unlike with finite-volume extra space, Newton's Law is modified at astronomically large distances. Dvali and Gabadadze [57] showed that this is not the case if the infinite space in which the brane lives has dimension D>5. They studied a three-brane of the -function type and showed that the graviton propagator has a four-dimensional momentum dependence on the brane even at low energies. This feature is expected to persist if the brane is of finite thickness (``fat'') in the transverse directions for phenomenologically relevant values of the momentum. For extremely low energies, a fat brane should lead to a higher-dimensional behavior of the propagator. This was discussed qualitatively in [57]. Dr. Siopsis and his student Chad Middleton presented a quantitative study of a fat brane in infinite volume extra space [59]. By linearizing gravity in the harmonic gauge, they arrived at an explicit form of the graviton propagator. First, they obtained the propagator for the trace of the metric field over the transverse directions. The trace is a scalar field from the four-dimensional brane point of view. This scalar then contributed to the four-dimensional graviton propagator as a source, in addition to the matter fields. This complicated the tensor structure of the graviton propagator which became momentum dependent. They explicitly obtained the solution for the graviton propagator and analyzed its momentum dependence and pole structure. They found two infinite towers of massive modes and tachyonic ghosts. In the thin-brane limit they recovered four-dimensional Einstein gravity on the brane [57]. A couple of months later, similar results were obtained by Dubovsky and Rubakov [60] using a slightly different model. It would be interesting to understand the origin of the tachyonic poles better and whether they constitute a fatal pathology of the model. |
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