By Antonios Papazoglou; University of Oxford
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Extra info for Brane-world multigravity
However, despite the fact that we particle interpretation for the quanta of h have chosen that gauge, the results that we obtain are bound to be the same as in the general case where there would be quadratic mixing between the modes, because of the five dimensional gauge invariance of the theory. 11) will consist in a set independent equations for the graviton and the scalars. 15) where c is an integration constant. 14), the spin-2 part, as expected, contains the four dimensional Pauli-Fierz (0) ˜ Lagrangian LP F (h) for the gravitons without the mass term (see Appendix A), plus a mass term coming from the dimensional reduction.
2) In order to find a specific form of the equations of motion we need to write a metric ansatz which will take in account the spacetime symmetries of the three-brane.
Moreover, we can safely extend the integration to infinity since the integral saturates very fast for m Γ/4 ≡ rc−1 ≪ kex . 68) The first part is the same as in the GRS model potential, whereas the second one is the first correction that comes from the fact that x− is still finite though very large. e. mn ≪ nπke−3x . 8: The behaviour of the coupling, a(m), in the limit of x− ≫ e2x . Three regions of interest are indicated. The region m > ms gives rise to short distance corrections. The m1 ≪ m ≪ mc region gives rise to 4D gravity at intermediate distances and 5D gravity at ultra large distances.