Perturbations of nested branes with induced gravity

Abstract

We study the behaviour of weak gravitational fields in models where a 4D brane is embedded inside a 5D brane equipped with induced gravity, which in turn is embedded in a 6D spacetime. We consider a specific regularization of the branes internal structures where the 5D brane can be considered thin with respect to the 4D one. We find exact solutions corresponding to pure tension source configurations on the thick 4D brane, and study perturbations at first order around these background solutions. To perform the perturbative analysis, we adopt a bulk-based approach and we express the equations in terms of gauge invariant and master variables using a 4D scalar-vector-tensor decomposition. We then propose an ansatz on the behaviour of the perturbation fields when the thickness of the 4D brane goes to zero, which corresponds to configurations where gravity remains finite everywhere in the thin limit of the 4D brane. We study the equations of motion using this ansatz, and show that they give rise to a consistent set of differential equations in the thin limit, from which the details of the internal structure of the 4D brane disappear. We conclude that the thin limit of the "ribbon" 4D brane inside the (already thin) 5D brane is well defined (at least when considering first order perturbations around pure tension configurations), and that the gravitational field on the 4D brane remains finite in the thin limit. We comment on the crucial role of the induced gravity term on the 5D brane.

Beyond the cosmological standard model

“…A similar cascading behavior of the force law was also obtained recently in a different codimensiontwo framework [782]. Closely related work on intersecting branes was discussed in [783][784][785] with somewhat different motivations. See [780,786,787] for studies of degravitation in the cascading framework, and [788] for self-accelerated solutions in this context.…”

Degravitation and the Cascading DGP Model

“…In the past years, several interesting properties of the model were uncovered, such as a better behaviour concerning ghost instabilities [12][13][14] than that of the pure codimension-2 set-up with induced gravity [15] (see, however, [16]). Moreover, it was proposed that the codimension-1 brane acts somehow as a regulator, rendering gravity finite at the codimension-2 brane even when its thickness tends to zero [17,18]. However, a mathematically clean proof of these properties, as well as the general investigation of exact solutions, were made impossible by the well-known issue that the thin limit of a codimension-2 brane is not well-defined [19].…”

Modified gravity, the Cascading DGP model and its critical tension

“…Furthermore, it can be shown that the thin limit of the ribbon brane (inside the already thin codimension-1 brane) is well dened [23]. It follows that, with this assumption about the hierarchy of the thicknesses, we can indeed work with thin branes and forget the internal structures.…”

“…These background solutions are most naturally expressed in a bulk-based approach, where the bulk metric is at and the codimension-1 embedding has a cusp at the codimension-2 brane [23].…”