Gravity in Extra Dimensions of Infinite Volume

In this thesis, we discuss various aspects of the Dvali-Gabadadze-Porrati (DGP) model in D-dimensions. Firstly, we generalize the DGP model, which consists of a delta-function type 3-brane embedded in an infinite volume bulk-space by allowing the 3-brane to have a finite thickness. We calculate the graviton propagator in the harmonic gauge both inside and outside the brane and discuss its dependence on the thickness of the brane. We obtain two infinite towers of massive modes and tachyonic ghosts. In the thin-brane limit, we recover the four-dimensional Einstein gravity behavior of the graviton propagator which was found in the delta-function treatment. We then examine the 4D worldvolume momentum dependence of the tensor structure.

Secondly, we address the van Dam-Veltman-Zakharov (vDVZ) discontinuity of the 5D DGP model which arises from the breakdown of the perturbative expansion at linear order. Following a suggestion by Gabadadze [hep-th/0403161], we implement a constrained perturbative expansion parametrized by brane gauge-like parameters. We obtain the solution for the metric perturbations, explore the parameter space and show that the DGP solution exhibiting the vDVZ discontinuity corresponds to a set of measure zero. Thirdly, we discuss the weak-field Schwarzschild solution in the DGP model. By keeping up to second-order off-diagonal terms of the metric ansatz, we arrive at a perturbative expansion which is valid both far from and near the Schwarzschild radius. We calculate the lowest-order contribution explicitly and obtain the form of the metric both on the brane and in the bulk. As we approach the Schwarzschild radius, the perturbative expansion yields the standard four-dimensional Schwarzschild solution on the brane which is non-singular in the decoupling limit. This non-singular behavior is similar to the Vainshtein solution in massive gravity demonstrating the absence of the vDVZ discontinuity of the DGP model.